To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

Question

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Answer 1

Question

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

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Answer 2

Question

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

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Answer 3

Question

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

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Answer 4

Question

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

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Answer 5

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

Answer 6

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

Answer 7

Chapter 28, Problem 28.13AYK

(a)

To determine

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

Answer 8

(a)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=−578.758+14.307x1+113.50x2 .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	2	6229332	3114666	396.095	1.35E-32
Residual	53	416761.9	7863.433
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	-578.758	43.66725	-13.2538	1.85E-18
Length	14.30738	5.658797	2.528344	0.014475
Width	113.4997	30.26474	3.750227	0.000439

Thus, from above the multiple regression equation is as:

y^=b0+b1x1+b2x2⇒y^=−578.758+14.307x1+113.50x2

Answer 13

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

Answer 14

(b)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (a).

Answer 15

(b)

Expert Solution

Answer to Problem 28.13AYK

Only 93.73% of the variation in the weight of perch is explained by the model in part (a).

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. We will use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with two explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.968139
R Square	0.937292
Adjusted R Square	0.934926
Standard Error	88.676
Observations	56

As we can see that R2=93.73% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (a).

Answer 20

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 21

(c)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 22

(c)

Expert Solution

Answer to Problem 28.13AYK

The ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 27

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

Answer 28

(d)

To determine

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

Answer 29

(d)

Expert Solution

Answer to Problem 28.13AYK

The individual t tests indicate that both β1 and β2 are significantly different from zero.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (a), we can say that the P-values of both the β1 and β2 are significantly smaller than the level of significance then it means that we can reject the null hypothesis and there is statistical significance and that implies the individual t tests indicate that both β1 and β2 are significantly different from zero.

Answer 34

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

Answer 35

(e)

To determine

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

Answer 36

(e)

Expert Solution

Answer to Problem 28.13AYK

The estimated multiple regression equationis y^=113.935−3.483x1−94.631x2+5.241x1x2 .

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

ANOVA
	df	SS	MS	F	Significance F
Regression	3	6544330	2181443	1114.68	3.75E-47
Residual	52	101764.7	1957.013
Total	55	6646094

	Coefficients	Standard Error	t Stat	P-value
Intercept	113.9349	58.78439	1.938183	0.058039
Length	-3.48269	3.152101	-1.10488	0.274298
Width	-94.6309	22.29543	-4.24441	9.06E-05
interaction	5.241238	0.413121	12.68693	1.52E-17

And the estimated multiple regression equation with the term interaction is as:

y^=b0+b1x1+b2x2+b3x1x2⇒y^=113.935−3.483x1−94.631x2+5.241x1x2

In this, x1x2 refer to the term interaction of both the variables.

Answer 41

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

Answer 42

(f)

To determine

To explain how much of the variation in the weight of perch is explained by the model in part (e).

Answer 43

(f)

Expert Solution

Answer to Problem 28.13AYK

98.47% of the variation in the weight of perch is explained by the model in part (e).

Answer 44

(f)

Expert Solution

Answer 45

(f)

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. Now, we will create a new variable called interaction by multiplying the two explanatory variables, length and width and use the Excel software to find the regression analysis by the data analysis option in the data tab. Now, the estimated regression model with three explanatory variables, length and width, to predict perch is as:

Regression Statistics
Multiple R	0.992314
R Square	0.984688
Adjusted R Square	0.983805
Standard Error	44.23814
Observations	56

Since in this we have R2=98.47% that is the coefficient of determination and this explains the variation in the weight of perch is explained by the model in part (e).

Answer 48

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 49

(g)

To determine

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 50

(g)

Expert Solution

Answer to Problem 28.13AYK

Yes, the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 51

(g)

Expert Solution

Answer 52

(g)

Expert Solution

Answer 53

Expert Solution

Answer 54

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e), we can say from the analysis that the test statistics value of F is more than the critical value of F , then it means that we can reject the null hypothesis and there is statistical significance and this explains that the ANOVA table indicates that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer 55

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

Answer 56

(h)

To determine

To describe how the individual t statistics changed when the interaction term was added.

Answer 57

(h)

Expert Solution

Explanation of Solution

In the question, it is given the table that contains data on the size of perch caught in a lake in Finland. From part (e) and (a), we can say from the analysis that when the interaction term is added to the model then the individual t statistics becomes negative and decreased from that of part (a) and also in part (e) one of the P-values for the slope is larger than the level of significance that means it is not statistically significant but in part (a), both the slopes were statistically significant.

Answer 58

(h)

Expert Solution

Answer 59

(h)

Expert Solution

Answer 60

Expert Solution

Answer 61

Ch. 28 - Prob. 28.1AYK Ch. 28 - Prob. 28.2AYK Ch. 28 - Prob. 28.3AYK Ch. 28 - Prob. 28.4AYK Ch. 28 - Prob. 28.5AYK Ch. 28 - Prob. 28.6AYK Ch. 28 - Prob. 28.7AYK Ch. 28 - Prob. 28.8AYK Ch. 28 - Prob. 28.9AYK Ch. 28 - Prob. 28.10AYK

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

To find out the estimated multiple regression equation and model to predict the weight of a perch by two explanatory variables.

Answer to Problem 28.13AYK

Explanation of Solution

To explain how much of the variation in the weight of perch is explained by the model in part (a).

Answer to Problem 28.13AYK

Explanation of Solution

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer to Problem 28.13AYK

Explanation of Solution

To explain do the individual t tests indicate that both β1 and β2 are significantly different from zero.

Answer to Problem 28.13AYK

Explanation of Solution

To create a new variable called interaction and use the multiple regression model with three explanatory variables to predict weight of a perch and the estimated multiple regression equation.

Answer to Problem 28.13AYK

Explanation of Solution

To explain how much of the variation in the weight of perch is explained by the model in part (e).

Answer to Problem 28.13AYK

Explanation of Solution

To explain does the ANOVA table indicate that at least one of the explanatory variables is helpful in predicting the weight of perch.

Answer to Problem 28.13AYK

Explanation of Solution

To describe how the individual t statistics changed when the interaction term was added.

Explanation of Solution

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