The data provided give the gasoline mileage? (in miles per? gallon) based on the

Question

The data provided give the gasoline mileage? (in miles per? gallon) based on the horsepower of a? car's engine,

Upper X 1 commaX1,

and the weight of the? car,

Upper X 2 commaX2,

?(in pounds). Perform a multiple regression analysis using the data and determine the VIF for each independent variable in the model. Is there reason to suspect the existence of? collinearity?

MPG Horsepower Weight

15.6 189 4,748

19.5 108 3,530

20.7 144 3,200

18.3 173 4,448

17.3 165 4,290

27.4 76 3,192

44.4 65 2,113

27.2 86 2,486

28.1 84 2,602

21.5 135 3,866

Explanation / Answer

Here MPG is the dependent variable and horsepower ans weight are independent variables.

This is the problem of multiple regression since there are two independent variables.

We haveto fit multiple regression of weight on mpg and horsepower.

We can do multiple regression in XLSTAT.

steps :

ENTER data into excel sheet --> Modeling data --> Linear regression --> Y : select weight data -> X : Select horsepower and mpg data --> Outputs : select all the apply --> ok

This will be the output.

We can see that in the regression equation one coefficient is negative and one coefficient is positive.

Also we can see that from the F-test overall model is significant at 5% level of significance.

From the t-test mpg is insignificant variable and horsepower is significant variable.

We can include significant variable into the model and exclude insignificant variables from the model.

Rsq = 0.872

It expresses the proportion of variation in y which is explained by variation in x's.

VIF for mpg and horsepower is 3.048

There is multicollinearity occures.

Summary statistics: Variable Observations Obs. with missing data Obs. without missing data Minimum Maximum Mean Std. deviation weight 10 0 10 2113.000 4748.000 3447.500 890.121 mpg 10 0 10 15.600 44.400 24.000 8.433 horsepower 10 0 10 65.000 189.000 122.500 44.585 Correlation matrix: mpg horsepower weight mpg 1 -0.820 -0.851 horsepower -0.820 1 0.918 weight -0.851 0.918 1 Multicolinearity statistics: mpg horsepower Tolerance 0.328 0.328 VIF 3.048 3.048 Regression of variable weight: Summary of the variables selection weight: Nbr. of variables Variables MSE R² Adjusted R² Mallows' Cp Akaike's AIC Schwarz's SBC Amemiya's PC 2 mpg / horsepower 130325.939 0.872 0.836 3.000 120.211 121.119 0.185 The best model for the selected selection criterion is displayed in blue Goodness of fit statistics (weight): Observations 10.000 Sum of weights 10.000 DF 7.000 R² 0.872 Adjusted R² 0.836 MSE 130325.939 RMSE 361.007 MAPE 7.735 DW 2.103 Cp 3.000 AIC 120.211 SBC 121.119 PC 0.238 Analysis of variance (weight): Source DF Sum of squares Mean squares F Pr > F Model 2 6218552.927 3109276.464 23.858 0.001 Error 7 912281.573 130325.939 Corrected Total 9 7130834.500 Computed against model Y=Mean(Y) Model parameters (weight): Source Value Standard error t Pr > |t| Lower bound (95%) Upper bound (95%) Intercept 2571.624 1126.691 2.282 0.056 -92.577 5235.825 mpg -31.832 24.911 -1.278 0.242 -90.738 27.074 horsepower 13.386 4.712 2.841 0.025 2.244 24.529 Equation of the model (weight): weight = 2571.62415194152-31.8319821215007*mpg+13.3864768895877*horsepower

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