1.Fit a multiple regression model for gasoline mileage as it depends on engine horsepower, vehicle weight, and the type of transmission (the "predictor" variables).

a.In a new line entered below this part, state the multiple regression equation, including your definitions of the variables.

b.In a new space entered below this part, insert a copy of the regression report.

c.In a new line entered below this part, explicitly define your coding of the "transmission" variable.

2.a.In new line entered below this part, state in words the specific meaning of the numerical value of the regression coefficient on engine horsepower in terms of what it measures for this problem. (In other words, what does this number measure and how much?)

b.In a new line entered below this part, state whether or not this coefficient makes sense according to what you would expect for it. Include a brief explanation for your response.

3.a.In a new line entered below this part, state 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?)

b.In a new line entered below this part, state whether or not this coefficient makes sense, according to what you would expect for it. Include a brief explanation for your response

4.a.In a new line entered below this part, state in words the specific meaning of the numerical value of the regression coefficient on transmission type in terms of what it measures for this problem. (In other words, what does this number measure and how much?)

b.In a new line entered below this part, state whether or not this coefficient has any practical meaning in the context of this problem. Include a brief explanation for your response.

5.a.In a new line entered below this part, state in words the specific meaning of the numerical value of the "Intercept" regression coefficient in terms of what it measures for this problem. (In other words, what does this number measure and how much?)

b.In a new line entered below this part, state whether or not this coefficient has any practical meaning in the context of this problem?Explain.

6.a.In a new line entered below this part, state the overall significance of this multiple regression. State the specific statistic or statistics that were used and how they were used. Finally, conclude whether or not this model is overall significant and state why.

b.In a new line entered below this part, state whether or not the coefficient on each individual predictor variable is significant. Explain your conclusion for each variable, including the specific statistic or statistics that were used and how they were used.

7.a.In a new line entered below this part, state the numerical value of the coefficient of determination for this model.

b.In new lines entered below this part, show that this coefficient is numerically equal to SSR/SST.

c.In a new line entered below this part, state the numerical value of the adjusted coefficient of determination for this model.

d.In a new line entered below this part, state what the adjusted coefficient of determination is adjusted for in the specific context of this problem,

e.In a new line entered below this part, state how much of the variation in mpg is fairly and truthfully represented by this model.

f.In a new line entered below this part, state how much of the variation in mpg is NOT fairly and truthfully represented by this model.

8.a.In a space created below this part, insert a copy of the plot of the residuals of this model against its fitted values.

b.In a new line entered below this part, describe the appearance of this residual plot.

c.In a new line entered below this part, state the RMSE of this regression.

9.a.In a new line entered below this part, state the gasoline mileage (in mpg) predicted for a vehicle that has a 105-horsepower engine, weighs 3380 pounds, and has a manual transmission.

b.In a new line entered below this part, state the numerical value of 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.In a new line entered below this part, 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.

10.a.In a new line entered below this part, state the gasoline mileage (in mpg) predicted for a vehicle that has a 135-horsepower engine, weighs 2650 pounds, and has an automatic transmission.

b.In a new line entered below this part, state a 95% prediction interval for your prediction in part 10.a.

11.a.In a new space entered below this part, calculate and present the correlation matrix.

b.In a new line entered below this part, based only on your correlation matrix calculated and presented in part 11.a, state the strength of the correlations between the predictor variables.

c.In a new line entered below this part, based only on your correlation matrix calculated and presented in part 11.a, state which, if any, of any of the predictor variables are correlated with each other to such an extent that you suspect that they are not truly independent of each other.

d.In a new line entered below this part, based only on your correlation matrix calculated and presented in part 11.a, state whether or not multicollinearity an issue in this problem and why.

e.In a new line entered below this part, based only on your answer to part 11.d, state whether or not any of the predictor variables should be deleted and why.

e.In a new line entered below this part, based only on your answer to part 11.e, state which predictor variable or variables you recommend for deletion and why.Also state which predictor variable or variables you recommend to retain and why.

12.a.In a new line entered below this part, calculate and state the variance inflation factor, VIF, for each predictor variable.

b.In a new line entered below this part, based on only VIF, state which, if any, of the predictor variables are related to each other to such an extent that you suspect that they are not truly independent of each other (and explain why).

c.In a new line entered below this part, based on only VIF, state whether or not multicollinearity a problem and why.

d.In a new line entered below this part, based on only VIF, state whether you recommend deleting any of the predictor variables.

e.In a new line entered below this part, based only on VIF, state which predictor variable or variables you recommend for deletion and why.Also state which predictor variable or variables you recommend to retain.

13.Perform another multiple regression model for gasoline mileage as it depends on the set of predictor variables retained from part 12.e (use the same definitions of the variables as you used in part 1).

a.In a new space entered below this part, insert a copy of the regression report.

b.In a new line entered below this part, state the equation of this multiple regression.

c.In a new line entered below this part, state the overall significance of this multiple regression. State the specific statistic or statistics that were used and how they were used. Finally, conclude whether or not this model is overall significant and state why.

d.In a new line entered below this part, state whether or not each individual variable coefficient is significant. Explain your conclusion for each variable, including the specific statistic or statistics that were used and how they were used.

e.In a new line entered below this part, state how much of the variation in mpg is fairly represented by this model.

14.a.In a new line entered below this part, insert a copy of the plot of the residuals of this model against its fitted values.

b.In a new line entered below this part, describe the appearance of this residual plot.

c.In a new line entered below this part, state here the RMSE of this regression.

15.Perform simple linear regression model for gasoline mileage as it depends on horsepower alone.

a.In a new line entered below this part, insert a copy of the regression output in a space created BELOW.

b.In a new line entered below this part, state here this simple linear regression equation.

c.In a new line entered below this part, state the overall significance of this simple linear regression. State the specific statistic or statistics that were used and how they were used. Finally, conclude whether or not this model is overall significant and state why.

d.In a new line entered below this part, state whether or not the coefficient of the predictor variable is significant. Explain your conclusion for each variable, including the specific statistic or statistics that were used and how they were used Comment on the significance of the variable coefficient.

e.How much of the variation in mpg is fairly represented by this model?

16.a. In a new space entered below this part, insert a copy of the plot of the residuals of this model against its fitted values.

b. In a new line entered below this part, describe here the appearance of this residual plot.

c. In a new line entered below this part, state the RMSE of this regression.

17.You have now found three regression models: the multiple regression model in part 1, another multiple regression model in 13, and the simple linear regression in part 15.

a. In new lines entered below this part, list here the RMSE for each of these regressions and compare them. Specifically, state which method has the lowest value of RMSE.

b. In a new line entered below this part, list the appropriate coefficient of determination for each of these regressions and compare them. Specifically, state which model has the highest value of these coefficients.

18.On the basis of your results in part 17, in a new line entered below this part, state the best possible regression equation to model gasoline mileage. Include the reason for your decision.

19.In a new line entered below this part, with the best regression model found in part 18, repeat the prediction in parts 9 and 10, if necessary.

MPG Horsepower 43.1 19.9 19.2 17.7 18.1 20.3 21.5 16.9 15.5 18.5 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 48 110 105 165 139 103 115 155 142 150 71 76 65 100 84 58 88 92 139 110 1685 3365 3535 3445 3205 2830 3345 4360 4054 3940 2190 2044 2110 2420 2490 1455 2305 2465 3570 3155 _ | Weight Transmission manual manual manual manual manual manual automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic manual 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 20.5 28.0 34.7 36.1 35.7 20.2 23.9 29.9 30.4 36.0 22.6 36.4 27.5 33.7 44.6 32.9 38.0 24.2 38.1 39.4 25.4 110 90 63 66 80 85 90 65 67 74 110 87 95 75 67 100 67 120 60 70 116 3155 2678 2015 1800 2015 2965 2920 2380 2850 1980 2800 2950 2560 1910 1850 2615 1965 3230 1968 2070 2985 manual manual manual manual manual manual manual manual automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic automatic 41 25.4 116 2985 automatic 42 31.3 75 1842 automatic 43 34.1 68 1985 automatic 44 34.0 88 2395 automatic 45 31.0 82 2720 automatic 46 27.4 80 2470 manual 47 22.3 88 2890 manual - - - 48 28.0 79 2025 manual 49 17.6 85 3465 manual 50 34.4 65 3465 manual 51 20.6 105 3380 manual