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.© BrainMass Inc. brainmass.com October 17, 2018, 11:27 am ad1c9bdddf
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.
City Length Width Weight Japan
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.
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 ...
Multiple regression in City MPG is examined.
Multiple Regression Equation: Example Problems
See file attached for data charts associated with each question.
a) A bicycle company wants to measure the effectiveness of different types of advertising media in the promotion of its new bicycle. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising. A sample of 22 cities with approximately equal population is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper adverting. The sales of the bicycle (in thousands of dollars ) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded.
Interpret the meaning of the regression coefficients, b0 (superscript 0)
What is the multiple regression equation?
b) A consumer organization wants to develop a regression model to predict gasoline mileage (MPG) based on the horsepower of the car's engine and the weight of the car in (pounds). A sample of 50 recents car models was selected, with the results shown at left.
Interpret the meaning of the slope for horsepower in this mode.
Predict the miles per gallon for a car that has 60 horsepower and weigh 2000 pounds.View Full Posting Details