Chapter 11, Problem 40E

To determine

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

Answer to Problem 40E

Solution: The regression equation is

${\text{VO}}^{-}=558+9.92\text{ OC}$

with $S=387.351$ and $R^2=20.7\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	1	1134474	1134474	7.56	0.010
Residual	29	4351193	150041
Total	30	5485667

Explanation of Solution

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

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

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

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

Step 5: Click “OK.”

The estimated regression equation is

${\text{VO}}^{-}=558+9.92\text{ OC}$

with $F=7.56$ and $P-\text{value}=0.010$.

Conclusion: Since the P-value is less than 0.05, the result is significant. The variation in the variable ${\text{VO}}^{-}$ is 20.7%.

To determine

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

Answer to Problem 40E

Solution: The regression equation is

${\text{VO}}^{-}=301+44.4\text{ TRAP}$

with $S=319.727$ and $R^2=46.0\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	1	2521128	2521128	24.66	0.000
Residual	29	2964539	102225
Total	30	5485667

Explanation of Solution

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

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

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

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

Step 5: Click “OK.”

The estimated regression equation is

${\text{VO}}^{-}=301+44.4\text{ TRAP}$

with $F=24.66$ 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 46.0%.

To determine

To test: A regression to predict the ${\text{VO}}^{-}$ using OC and TRAP.

Answer to Problem 40E

Solution: The Regression equation is

${\text{VO}}^{-}=309-1.87\text{OC+ }48.5\text{ TRAP}$

with $S=324.353$ and $R^2=46.3\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	2	2539934	1269967	12.07	0.000
Residual	28	2945733	105205
Total	30	5485667

Explanation of Solution

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

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{VO}}^{-}$ ” in Response and select “OC and TRAP” in Predictors.

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

Step 5: Click “OK.”

The estimated regression equation is

${\text{VO}}^{-}=309-1.87\text{OC+ }48.5\text{ TRAP}$

with $F=12.07$ 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 46.3%.

To determine

To test: A regression to predict the ${\text{VO}}^{-}$ using OC, TRAP, and ${\text{VO}}^{+}$.

Answer to Problem 40E

Solution: The regression equation is

${\text{VO}}^{-}=267-6.51\text{OC+ }9.48\text{TRAP+0}{\text{.724 VO}}^{+}$

with $S=179.162$ and $R^2=84.2\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	3	4618997	1539666	47.97	0.000
Residual	27	866669	32099
Total	30	5485667

Explanation of Solution

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

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

Step 3: Select “ ${\text{VO}}^{-}$ ” in Response and select “OC, TRAP and ${\text{VO}}^{+}$ ” in Predictors.

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

Step 5: Click “OK.”

The estimated regression equation is

${\text{VO}}^{-}=267-6.51\text{OC+ }9.48\text{TRAP+0}{\text{.724 VO}}^{+}$

with $F=47.97$ 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 ${\text{VO}}^{-}$ is 84.2%.

To determine

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

Answer to Problem 40E

Solution: The regression equation is

${\text{VO}}^{-}=298-5.25\text{OC+0}{\text{.778 VO}}^{+}$

with $S=179.688$ and $R^2=83.5\%$.

The ANOVA is given below:

	Degrees of freedom	Sum of Squares	Mean sum of squares	F-statistic	P-value
Regression	2	4581607	2290804	70.95	0.000
Residual	28	904060	32288
Total	30	5485667

Explanation of Solution

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

Step 1: Open the Minitab worksheet.

Step 2: Go to Stat > Regression > Regression.

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

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

Step 5: Click “OK.”

The estimated regression equation is

${\text{VO}}^{-}=298-5.25\text{OC+0}{\text{.778 VO}}^{+}$

with $F=70.95$ 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 83.5%.