(a) Answer The equation of the least-squares regression line is y ^ = − 2.9935 x + 157.68 There are 67.875 % of males that return after a season with 30 breeding pairs. Explanation Given: Calculation: From the above figure we can clearly see that slope ( b ) = − 2.9935 Y − intercept ( a ) = 157.68 Thus, the equation of the least-squares regression line is y ^ = − 2.9935 x + 157.68 The study records the percent of males (banded for identification) that returned the next breeding. This is the outcome of the study; the percent return is the response variable. Now, breeding pairs is a second variable. The entire purpose of the study is to determine how, if at all, breeding pairs affect the percent return. Breeding pairs is an explanatory variable. We will use breeding pairs (explanatory variable or predictor) to predict percent return (response or predicted variable). Percent return is the dependent variable and breeding pairs is the independent variable. The equation of the least-squares regression line for predicting the percent of males that return from the number of breeding pairs is. Percent return = 157.68 − 2.9935 (Breeding pairs) The percent of returning males after a season with 30 breeding pairs is, ( Predicted ) Percent return = 157.68 − 2.9935 × 30 = 67.875 There are 67.875 % of males that return after a season with 30 breeding pairs. Conclusion: Therefore, the equation of the least-squares regression line is y ^ = − 2.9935 x + 157.68 There are 67.875 % of males that return after a season with 30 breeding pairs. (b) To determine To find: percentage of variation explained by the regression line Answer The percentage of variation explained by the regression line is r 2 = 63.1 % Explanation Calculation: From the above figure we can clearly see that r 2 = 63.1 % We interpret this by saying that 63.1 % of the year-to-year variation in percent of returning males is explained by the straight line relationship with number of breeding pairs the previous year. Conclusion: Therefore, the percentage of variation explained by the regression line is r 2 = 63.1 % (c) To determine To find: the correlation of percent of returning males and breeding pairs and explain whether the sign of r is + or − ? Answer Percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is − 0.794 . Explanation Calculation: From the above figure we can clearly see that slope ( b ) = − 2.9935 This shows negative correlation between variables. R − s q ( R 2 ) = 63.1 % r 2 = 0.631 correlation ( r ) = r 2 = 0.631 = − 0.794 Percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is − 0.794 . Conclusion: Therefore, percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is − 0.794 . (d) To determine To interpret: the value of s Answer The predication of the percent returning is varied by about 9.46334 % from the actual percent returning. Explanation Calculation: For these data the standard deviation of the residuals: s = 9.46334 The standard deviation of the residuals s measures the average size of the prediction errors (residuals) when using the regression line, s = 9.46334 shows too much prediction error. Conclusion: Therefore, the predication of the percent returning is varied by about 9.46334 % from the actual percent returning.

The Practice of Statistics for AP - 4th Edition

4th Edition

ISBN: 9781429245593

Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.

Publisher: Macmillan Higher Education

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Question

Chapter 3.2, Problem 63E

(a)

To determine

To find: the equation of the least-squares regression line

(a)

Expert Solution

Answer to Problem 63E

The equation of the least-squares regression line is y^=−2.9935x+157.68

There are 67.875% of males that return after a season with 30 breeding pairs.

Explanation of Solution

Given:

The Practice of Statistics for AP - 4th Edition, Chapter 3.2, Problem 63E

Calculation:

From the above figure we can clearly see that slope(b)=−2.9935Y−intercept(a)=157.68

Thus, the equation of the least-squares regression line is y^=−2.9935x+157.68

The study records the percent of males (banded for identification) that returned the next breeding. This is the outcome of the study; the percent return is the response variable. Now, breeding pairs is a second variable. The entire purpose of the study is to determine how, if at all, breeding pairs affect the percent return. Breeding pairs is an explanatory variable. We will use breeding pairs (explanatory variable or predictor) to predict percent return (response or predicted variable). Percent return is the dependent variable and breeding pairs is the independent variable. The equation of the least-squares regression line for predicting the percent of males that return from the number of breeding pairs is.

Percent return =157.68−2.9935 (Breeding pairs)

The percent of returning males after a season with 30 breeding pairs is,(Predicted)Percent return=157.68−2.9935×30=67.875

There are 67.875% of males that return after a season with 30 breeding pairs.

Conclusion:

Therefore, the equation of the least-squares regression line is y^=−2.9935x+157.68

There are 67.875% of males that return after a season with 30 breeding pairs.

(b)

To determine

To find: percentage of variation explained by the regression line

(b)

Expert Solution

Answer to Problem 63E

The percentage of variation explained by the regression line is r2=63.1%

Explanation of Solution

Calculation:

From the above figure we can clearly see that r2=63.1%

We interpret this by saying that 63.1% of the year-to-year variation in percent of returning males is explained by the straight line relationship with number of breeding pairs the previous year.

Conclusion:

Therefore, the percentage of variation explained by the regression line is r2=63.1%

(c)

To determine

To find: the correlation of percent of returning males and breeding pairs and explain whether the sign of r is + or − ?

(c)

Expert Solution

Answer to Problem 63E

Percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is −0.794 .

Explanation of Solution

Calculation:

From the above figure we can clearly see that slope(b)=−2.9935

This shows negative correlation between variables.

R−sq(R2)=63.1%r2=0.631correlation(r)=r2=0.631=−0.794

Percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is −0.794 .

Conclusion:

Therefore, percent of returning males and breeding pairs are negatively correlated and the coefficient of correlation between them is −0.794 .

(d)

To determine

To interpret: the value of s

(d)

Expert Solution

Answer to Problem 63E

The predication of the percent returning is varied by about 9.46334 % from the actual percent returning.

Explanation of Solution

Calculation:

For these data the standard deviation of the residuals:

s=9.46334

The standard deviation of the residuals s measures the average size of the prediction errors (residuals) when using the regression line, s=9.46334 shows too much prediction error.

Conclusion: Therefore, the predication of the percent returning is varied by about 9.46334 % from the actual percent returning.

Chapter 3.2, Problem 62E

Chapter 3.2, Problem 64E

Chapter 3 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 3.1 - Prob. 1.1CYU Ch. 3.1 - Prob. 1.2CYU Ch. 3.1 - Prob. 2.1CYU Ch. 3.1 - Prob. 2.2CYU Ch. 3.1 - Prob. 2.3CYU Ch. 3.1 - Prob. 2.4CYU Ch. 3.1 - Prob. 2.5CYU Ch. 3.1 - Prob. 3.1CYU Ch. 3.1 - Prob. 3.2CYU Ch. 3.1 - Prob. 1E

Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.2 - Prob. 1.3CYU Ch. 3.2 - Prob. 1.4CYU Ch. 3.2 - Prob. 2.1CYU Ch. 3.2 - Prob. 3.1CYU Ch. 3.2 - Prob. 3.2CYU Ch. 3.2 - Prob. 3.3CYU Ch. 3.2 - Prob. 4.1CYU Ch. 3.2 - Prob. 4.2CYU Ch. 3.2 - Prob. 5.1CYU Ch. 3.2 - Prob. 5.2CYU Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - Prob. 47E Ch. 3.2 - Prob. 48E Ch. 3.2 - Prob. 49E Ch. 3.2 - Prob. 50E Ch. 3.2 - Prob. 51E Ch. 3.2 - Prob. 52E Ch. 3.2 - Prob. 53E Ch. 3.2 - Prob. 54E Ch. 3.2 - Prob. 55E Ch. 3.2 - Prob. 56E Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - Prob. 59E Ch. 3.2 - Prob. 60E Ch. 3.2 - Prob. 61E Ch. 3.2 - Prob. 62E Ch. 3.2 - Prob. 63E Ch. 3.2 - Prob. 64E Ch. 3.2 - Prob. 65E Ch. 3.2 - Prob. 66E Ch. 3.2 - Prob. 67E Ch. 3.2 - Prob. 68E Ch. 3.2 - Prob. 69E Ch. 3.2 - Prob. 70E Ch. 3.2 - Prob. 71E Ch. 3.2 - Prob. 72E Ch. 3.2 - Prob. 73E Ch. 3.2 - Prob. 74E Ch. 3.2 - Prob. 75E Ch. 3.2 - Prob. 76E Ch. 3.2 - Prob. 77E Ch. 3.2 - Prob. 78E Ch. 3.2 - Prob. 79E Ch. 3.2 - Prob. 80E Ch. 3.2 - Prob. 81E Ch. 3 - Prob. 1CRE Ch. 3 - Prob. 2CRE Ch. 3 - Prob. 3CRE Ch. 3 - Prob. 4CRE Ch. 3 - Prob. 5CRE Ch. 3 - Prob. 6CRE Ch. 3 - Prob. 7CRE Ch. 3 - Prob. 1PT Ch. 3 - Prob. 2PT Ch. 3 - Prob. 3PT Ch. 3 - Prob. 4PT Ch. 3 - Prob. 5PT Ch. 3 - Prob. 6PT Ch. 3 - Prob. 7PT Ch. 3 - Prob. 8PT Ch. 3 - Prob. 9PT Ch. 3 - Prob. 10PT Ch. 3 - Prob. 11PT Ch. 3 - Prob. 12PT Ch. 3 - Prob. 13PT

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