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# Multiple regression: City MPG

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Perform a complete multiple regression using City MPG as the response variables. Assess the model using the steps as performed/outlined (correlation matrix, f-test, t-tests, r-sq and standard error). If the full multiple regression needs modification, perform a stepwise regression and select the final model. Briefly note why you selected your final model. Interpret the coefficients of the final model only.

Please see the Excel file for the data.

https://brainmass.com/statistics/regression-analysis/multiple-regression-city-mpg-539906

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Perform a complete multiple regression using City MPG as the response variables. Assess the model using the steps as performed/outlined in class (correlation matrix, f-test, t-tests, r-sq and standard error). If the full multiple regression needs modification, perform a stepwise regression and select the final model. Briefly note why you selected your final model. Interpret the coefficients of the final model only.
Correlation Matrix
City Length Width Weight Japan
City 1
Length -0.631204198 1
Width -0.632927505 0.719811378 1
Weight -0.825196386 0.752597232 0.739273687 1
Japan -0.049485851 -0.160046674 -0.266866176 -0.093307413 1
From the correlation matrix it is clear that the highest correlation is between city and Weight.
Step 1
Now we can perform regression analysis with City as the dependent variable and Length, Width, Weight and Japan as the independent variables.
The estimated regression equation is given by,
City = 43.9932 - 0.0039 * Length - 0.1064 * Width - 0.0041 * Weight - 1.3228 * Japan
The model adequacy is measured using the R2 value. Here R2 = 0.7027. Thus 70.27% variability in City can be explained by the regression model.
Standard error of estimate = 2.5055
The overall utility of the suggested model is tested using F test.
Here F statistic is significant with p-value less than 0.05. Hence we can conclude that the suggested model is significant in predicting the dependent variable.
The regression coefficients can be tested using student's t distribution.
The regression coefficient Weight is significant, since the p-value is less than 0.05. But the variables Length, Width and Japan are not significant, since the respective p-values are greater than 0.05. That is, the variables Length, Width ...

#### Solution Summary

Multiple regression in City MPG is examined.

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See file attached for data charts associated with each question.

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