Chapter 11, Problem 41E

To determine

To test: A regression to predict the ${\text{LVO}}^{-}$ using LOC.

Answer to Problem 41E

Solution: The regression equation is

${\text{LVO}}^{-}=5.21+0.441\text{ LOC}$

with $S=0.4089$ and $R^2=30.8\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	1	2.1556	2.1556	12.89	0.001
Residual	29	4.8499	0.1672
Total	30	7.0055

Explanation of Solution

Calculation: To perform the regression analysis to predict L ${\text{VO}}^{-}$, Minitab is used. The steps to be followed are as follows:

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{LVO}}^{-}$ ” in Response and select “LOC” in Predictors.

Step 4: Go to graph and select residual versus fits.

Step 5: Click “OK.”

The estimated regression equation is

${\text{LVO}}^{-}=5.21+0.441\text{ LOC}$

with $F=12.89$ and $P\text{-value}=0.001$.

Conclusion: Since the P-value is less than 0.05, the result is significant. The variation in the variable ${\text{VO}}^{-}$ is 30.8%.

To determine

To test: A regression to predict the ${\text{LVO}}^{-}$ using LTRAP.

Answer to Problem 41E

Solution: The regression equation is

${\text{LVO}}^{-}=5.09+0.645\text{ LTRAP}$

with $S=0.3673$ and $R^2=44.1\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	1	3.0915	3.0915	22.91	0.000
Residual	29	3.9140	0.1350
Total	30	7.0055

Explanation of Solution

Calculation: To perform the regression analysis to predict ${\text{LVO}}^{-}$, Minitab is used. The steps to be followed are as follows:

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{LVO}}^{-}$ ” in Response and select “LTRAP” in Predictors.

Step 4: Go to graph and select residual versus fits.

Step 5: Click “OK.”

The estimated regression equation is

${\text{LVO}}^{-}=5.09+0.645\text{ LTRAP}$

with $F=22.19$ and $P\text{-value}=0.000$.

Conclusion: Since the P-value is less than 0.05, the result is significant. The variation in the variable ${\text{VO}}^{-}$ is 44.1%.

To determine

To test: A regression to predict the ${\text{LVO}}^{-}$ using LOC and LTRAP.

Answer to Problem 41E

Solution: The regression equation is

${\text{LVO}}^{-}=5.04+0.057\text{LOC+ }0.590\text{LTRAP}$

with $S=0.373250$ and $R^2=44.3\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	2	3.1047	1.5524	11.14	0.000
Residual	28	3.9008	0.1393
Total	30	7.0055

Explanation of Solution

Calculation: To perform the regression analysis to predict ${\text{LVO}}^{-}$, Minitab is used. The steps to be followed are as follows:

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{LVO}}^{-}$ ” in Response and select “LOC and LTRAP” in Predictors.

Step 4: Go to graph and select residual versus fits.

Step 5: Click “OK.”

The estimated regression equation is

${\text{LVO}}^{-}=5.04+0.057\text{LOC+ }0.590\text{LTRAP}$

with $F=11.14$ and $P\text{-value}=0.000$. For OC, t = 0.31 and $P\text{-value}=0.76$, and for TRAP, t = 2.61 and $P\text{-value}=0.014$.

Conclusion: Since the P-value is less than 0.05 for LTRAP, the result is significant for LTRAP. The variation in the variable ${\text{LVO}}^{-}$ is 44.3%.

To determine

To test: A regression to predict the ${\text{LVO}}^{-}$ using LOC, LTRAP, and ${\text{LVO}}^{+}$.

Answer to Problem 41E

Solution: The regression equation is

${\text{LVO}}^{-}=1.74-0.233\text{ LOC+ }0.0111\text{ LTRAP+0}{\text{.824 LVO}}^{+}$

with $S=0.2621$ and $R^2=73.5\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	3	5.1494	1.7165	24.97	0.000
Residual	27	1.8562	0.0687
Total	30	7.0055

Explanation of Solution

Calculation: To perform the regression analysis to predict ${\text{LVO}}^{-}$, Minitab is used. The steps to be followed are as follows:

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{LVO}}^{-}$ ” in Response and select “LOC, LTRAP and ${\text{LVO}}^{+}$ ” in Predictors.

Step 4: Go to graph and select residual versus fits.

Step 5: Click “OK.”

The estimated regression equation is

${\text{LVO}}^{-}=1.74-0.233\text{ LOC+ }0.0111\text{ LTRAP+0}{\text{.824 LVO}}^{+}$

with $F=24.97$ and $P\text{-value}=0.000$.

Conclusion: Since the P-value is less than 0.05, the result is significant. The variation in the variable ${\text{LVO}}^{-}$ is 73.5%.

To determine

To test: A regression to predict the ${\text{LVO}}^{-}$ using LOC and ${\text{LVO}}^{+}$.

Answer to Problem 41E

Solution: The Regression equation is

${\text{LVO}}^{-}=1.31-0.188\text{ LOC+0}{\text{.890 LVO}}^{+}$

with $S=0.2611$ and $R^2=72.8\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	2	5.0965	2.5483	37.38	0.000
Residual	28	1.9090	0.0682
Total	30	7.0055

Explanation of Solution

Calculation: To perform the regression analysis to predict ${\text{LVO}}^{-}$, Minitab is used. The steps to be followed are as follows:

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{LVO}}^{-}$ ” in Response and select “LOC and ${\text{LVO}}^{+}$ ” in Predictors.

Step 4: Go to graph and select residual versus fits.

Step 5: Click “OK.”

The estimated regression equation is

${\text{LVO}}^{-}=1.31-0.188\text{ LOC+0}{\text{.890 LVO}}^{+}$

with $F=37.38$ and $P\text{-value}=0.000$.

Conclusion: Since the P-value is less than 0.05, the result is significant. The variation in the variable ${\text{LVO}}^{-}$ is 72.8%.