We previously considered building multiple linear regression models for gas mileage of cars based on characteristics of each vehicle model. We can now consider a few different models and attempt to determine which model is better. (a) (4 points) Using the table of summary values below, and that we have taken a sample of 30 vehicles, compute the AIC for each of the three models. Based on these values, which model would you say is better? Residual Standard Error 3.227 Model Predictors Model 1 all 11 predictors Displacement, Horsepower, Torque, Number of Model 2 Trans oder Transmission Speeds, Weight Model 3 Displacement, Horsepower, Weight 3.245 3.171 (b) (4 points) Using the above summary table, calculate the corrected AIC for each of the above models. Based on this, would we prefer the same model as in part (a)? (c) (4 points) Now, knowing that the sample variance of gas mileage is 39.28 MPG, find the adjusted coefficient of determination for each of the models in (a). Based on this measure, which model is preferred? (d) (4 points) Suppose we consider the smallest model (model 3 from part (a)). We can fit a model using each predictor as a response using the remaining predictors as predictors. Below is a summary of each of these models. Response Displacement Horsepower Weight Predictors Horsepower, Weight Displacement, Weight Displacement, Horsepower Residual SE Sample Variance of Response 27.21 13511.05 15.64 1993.689 299.1 885420.2 Find the Variance Inflation Factor of each predictor. Should we be concerned about multi- collinearity in the model 3 from (a)? We previously considered building multiple linear regression models for gas mileage of cars based on characteristics of each vehicle model. We can now consider a few different models and attempt to determine which model is better. (a) (4 points) Using the table of summary values below, and that we have taken a sample of 30 vehicles, compute the AIC for each of the three models. Based on these values, which model would you say is better? Residual Standard Error 3.227 Model Predictors Model 1 all 11 predictors Displacement, Horsepower, Torque, Number of Model 2 Trans oder Transmission Speeds, Weight Model 3 Displacement, Horsepower, Weight 3.245 3.171 (b) (4 points) Using the above summary table, calculate the corrected AIC for each of the above models. Based on this, would we prefer the same model as in part (a)? (c) (4 points) Now, knowing that the sample variance of gas mileage is 39.28 MPG, find the adjusted coefficient of determination for each of the models in (a). Based on this measure, which model is preferred? (d) (4 points) Suppose we consider the smallest model (model 3 from part (a)). We can fit a model using each predictor as a response using the remaining predictors as predictors. Below is a summary of each of these models. Response Displacement Horsepower Weight Predictors Horsepower, Weight Displacement, Weight Displacement, Horsepower Residual SE Sample Variance of Response 27.21 13511.05 15.64 1993.689 299.1 885420.2 Find the Variance Inflation Factor of each predictor. Should we be concerned about multi- collinearity in the model 3 from (a)