Question

SUMMARY OUTPUT Dependent X variable: all other variables Regression Statistics Independent Y variable: oil usage Multiple...

SUMMARY OUTPUT
Dependent X variable: all other variables
Regression Statistics Independent Y variable: oil usage
Multiple R 0.885464
R Square 0.784046 variation
Adjusted R Square 0.76605
Standard Error 85.4675
Observations 40
ANOVA
df SS MS F Significance F
Regression 3 954738.9 318246.3089 43.56737 4.55E-12
Residual 36 262969 7304.693706
Total 39 1217708
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -218.31 63.95851 -3.413304572 0.001602 -348.024 -88.596 -348.024 -88.596
Degree Days 0.275079 0.036333 7.571119093 5.94E-09 0.201393 0.348765 0.201393 0.348765
Home Index 86.98875 9.630435 9.032691554 8.75E-11 67.45732 106.5202 67.45732 106.5202
Number People 5.26724 10.56179 0.498706879 0.62102 -16.1531 26.68755 -16.1531 26.68755

[10] The multiple regression model suggests that about 78% of the variation in the predictors can be explained by Oil Usage. True or False

I believe the statement is FALSE because Oil usage (independent variable) is explained by the 78% variation in the predictors (dependent variables) not as the question states. Please confirm if I'm right and explain if not, thanks!

Math   Statistics-And-Probability   
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Answer #1

Answer: False

Explanation:

Given statement is false. We know that the coefficient of determination for the regression model always shows the variation in the dependent variable due to independent variables. So, correct statement is given as below:

The multiple regression model suggests that about 78% of the variation in the dependent variable Oil usage can be explained by predictors.

Dependent Variable: Oil usage

Independent variables or predictors: Degree Days, Home Index, Number People

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