1 Find a multiple regression model that uses three (3) predictor variables to pr

Question

1 Find a multiple regression model that uses three (3) predictor variables to predict GHG emissions. The goal is to find a model that is the most accurate and efficient. 2 Show the data and statistics for your final choice on this page. Copy the adjusted r-square and p-value, and type out the regression equation that could be used to predict 3 greenhouse gas emissions 4 Pedictor Variables/Data Multiple Regression Summary Out 10 12 13 16 17 18 19 20 21 23 25 26 28 29 30 Adjusted R P-Value Regression Equation:

Explanation / Answer

Suppose we assume that dependent variable is greenhouse gas emissions and independent variables are gas mpg city driving, gas mpg highway driving and engine displacement.

This is the problem of multiple regression.

We can do multiple regression in excel.

steps :

ENTER data into EXCEL sheet --> Data --> Data analysis --> Regression --> ENTER --> Input Y range : select dependent variables range --> Input X range : select independent variables range --> Labels --> Output range : select one empty cell --> ok

Output is,

The regression equation is,

y = 10.915 + 0.505* engine displacement - 0.113*gas mpg city driving - 0.070*gas mpg highway driving

Rsq = 0.939256 = 93.9256%

Adj Rsq = 0.928536 = 92.8536%

We can see that overall model is significant because P-value for F-test is 0.0000 which is less than alpha (0.05).

Also by using individual significance gas mpg city driving and gas mpg highway driving are insignificant variables because p-value is greator than alpha (0.05).

And engine displacement is significant variable.

SUMMARY OUTPUT Regression Statistics Multiple R 0.969152 R Square 0.939256 Adjusted R Square 0.928536 Standard Error 0.329599 Observations 21 ANOVA df SS MS F Significance F Regression 3 28.55605 9.518684 87.62029 1.53E-10 Residual 17 1.846805 0.108636 Total 20 30.40286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 10.91517 1.03507 10.54535 7.07E-09 8.731362 13.09897 8.731362 13.09897 engine displacement 0.50514 0.121939 4.142549 0.000681 0.24787 0.76241 0.24787 0.76241 gas mpg city driving -0.11283 0.076226 -1.48016 0.157125 -0.27365 0.047996 -0.27365 0.047996 gas mpg highway driving -0.06981 0.059829 -1.16686 0.259375 -0.19604 0.056416 -0.19604 0.056416

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