An analyst at a consumer organization must develop a regression model to predict fuel economy (also referred to as gasoline mileage) of automobiles measured in miles per gallon (mpg) based on the horsepower of its engine, the weight of the car (in pounds) and the type of transmission (manual or automatic). The data for 50 randomly selected automobiles is presented in the table below. Fit a multiple regression model for gasoline mileage as it depends on engine horsepower, vehicle weight, and the type of transmission.
1) To do the regression equation we do the following steps in MINITAB:
1. Enter the given values in different columns.
2. Go to “Stat” then “Regression” then “Regression” then “Fit regression model”.
3. Enter MPG in “response” and HorsePower, Weight, Transmission in “continuous predictor”.
4. Click OK.
Thus we get the following output:
MPG = 55.19 - 0.1404 Horsepower - 0.00471 Weight - 3.35 Transmission
The definitions of the variables are fuel economy (also referred to as gasoline mileage) of automobiles measured in miles per gallon (mpg) based on the horsepower of its engine, the weight of the car (in pounds) and the type of transmission (manual or automatic).
2) Here we have to present a copy of the multiple regression output:
Analysis of Variance
Source DF
Adj SS Adj MS F-Value P-Value
Regression 3 2409.1
803.04 42.82 0.000
Horsepower 1 224.9
224.86 11.99 0.001
Weight
1 154.3 154.30
8.23 0.006
Transmission 1 121.9
121.90 6.50 0.014
Error
46 862.7 18.75
Total
49 3271.8
Model Summary
S R-sq
R-sq(adj) R-sq(pred)
4.33070 73.63%
71.91% 67.46%
Coefficients
Term
Coef SE Coef T-Value P-Value VIF
Constant
55.19 2.51
22.01 0.000
Horsepower -0.1404
0.0405 -3.46 0.001 3.17
Weight -0.00471
0.00164 -2.87 0.006 3.25
Transmission -3.35
1.31 -2.55 0.014 1.08
Regression Equation
MPG = 55.19 - 0.1404 Horsepower - 0.00471 Weight - 3.35 Transmission
Fits and Diagnostics for Unusual Observations
Std
Obs MPG Fit Resid Resid
4 17.70 12.47 5.23
1.45 X
13 46.60 36.14 10.46 2.48 R
49 34.40 26.41 7.99 2.18 R X
R Large residual
X Unusual X
3) Here we consider the transmission variable as a dummy variable
so to compute the coefficient for regression we take manual=1 and
automatic=0 and make the column transmission.
An analyst at a consumer organization must develop a regression model to predict fuel economy (also...
a.Predict the gasoline mileage for a vehicle that has a 105 horsepower engine, weighs 3380 pounds, and has a manual transmission. b.What is the residual in gasoline mileage between the mpg calculated in part 9.a and the actual gasoline mileage for this vehicle as listed in the data table? c.State two reasons why the result calculated in part 9.a is different from the actual gasoline mileage for this vehicle as listed in the data table. Transmission manual MPG 43.1 19.9...
Perform simple linear regression model for gasoline mileage as it depends on horsepower alone. Present a copy of this regression output report. a.State (here) this simple linear regression equation. b.Overall, is this regression significant? Choose yes or no and explain the reason for your choice. c.Comment on the significance of the variable coefficient. d.How much of the variation in mpg is fairly represented by this model? MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142...
Perform another multiple regression model for gasoline mileage as it depends on the set of independent variables retained from part 12.e (use the same definitions of the variables as you used in part 1). • Present a copy of this regression output report. a.State (here) this multiple regression equation. b.Overall, is this regression significant? c.Comment on the significance of each individual variable coefficient. d.How much of the variation in mpg is fairly represented by this model? a.Present the plot of...
a.Present (here) the plot of the residuals of this simple linear regression model against its fitted values. b. Describe (here) the appearance of this residual plot. c.State (here) the RMSE of this regression. MPG 43.1 19.9 19.2 Horsepower 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 110 90 17.7 18.1 20.3 21.5 16.9 ISS 185 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7...
a.Overall, is this regression significant? Yes or no? Explain, including the specific statistic or statistics that were used and how they were used. b.Is each individual variable coefficient significant? Yes or no for each variable. Explain for each variable, including the specific statistic or statistics that were used and how they were used. 7.a.State (here) the value of the coefficient of determination for this model. b.Show (here) that this coefficient is numerically equal to SSR/SST. c.State (here) the value of...
Use excels data analysis tool to preform a regression on the following set on numbers. Post your results. Then answer the following questions. A consumer Organization want to develop a regression model to predict gasoline mileage (as measured by miles per gallon) based on horsepower of the car's engine and the weight of the car, in pounds. A sample of 50 percent recent car models was selected, with the results recorded. 1. State the multiple regression equation. 2. Interpret the...
a.State (here) in words the specific meaning of the numerical value of the regression coefficient on engine horsepower in terms of what it measuresfor this problem. Does this coefficient make sense, according to what you would expect for it? b.State (here) in words the specific meaning of the numerical value of the regression coefficient on weight in terms of what it measures for this problem. (In other words, what does this number measure and how much?) • Does this coefficient...
a.Calculate and present the variance inflation factor, VIF, for each predictor variable. b.Based on VIF, which, if any, of any of the independent variables are related to each other such an extent that you suspect that they are not truly independent of each other. Why? c.Based on VIF, is multicollinearity a problem? Briefly explain why? d.If your answer to part 12.c is “yes,” do you recommend deleting any of the predictor variables? e.If your answer to part 12.d is “yes,”...
9. a. Predict the gasoline mileage for a vehicle that has a 105 horsepower engine, weighs 3380 pounds, and has a manual transmission. Manual: MPG (Y) = 51.77 - 0.1437 Horsepower (X1) - 0.00460 Weight (X2) = 51.77-0.1437(105)-0.00460(3380) = 21.133 b. What is the residual in gasoline mileage between the mpg calculated in part 9.a and the actual gasoline mileage for this vehicle as listed in the data table? c. State two reasons why the result calculated in part 9.a...
Please help with regression problem! Multiple choice A researcher is interested to find out how the engine displacement vehicle weight, and the type of transmission [i.e. automatic & manual] affect the automobile gasoline mileage. Type of transmission is represented by one dummy variable: automatic (-1, if transmission is automatic; 0, if transmission is manual) Part of the raw data and the regression output of 40 different car models are given below. cementícubic Weightlb)l Trans Automobile Miles/gallon Displacement(cubic in) Corvette 22.50...