(d) adjusted coefficient of determination for each of the models in (a). Based on this measure, which model is preferred? Now, knowing that the sample variance of gas mileage is 39.28 MPG, find the

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An engineer is interested in finding a model that can explain the variation in gas mileage of cars (Y,
in miles per gallon) using various characteristics of each vehicle model. The engineer has 11 vehicle
characteristics to consider as possible predictors to build a multiple linear model: Engine Displace-
ment, Horsepower, Torque, Compression ratio, Rear axle ratio, Carburetor, Number of transmission
speeds, overall length, width, weight, and Type of transmission (automatic or manual). We can
now consider a few different models and attempt to determine which model is better.
(a)
taken a sample of 30 vehicles, compute the AIC for each of the three models presented. Based
on these values, which model would you say is better?
Using the table of summary values below for 3 different models, and that we have
Model
Predictors included in each model
Residual Standard Error
all 11 predictors
Displacement, Horsepower, Torque, Number of
Transmission Speeds, Weight
Model 1
3.227
Model 2
3.245
Model 3 Displacement, Horsepower, Weight
3.171
(b)
models. Based on this, would we prefer the same model as in part (a)?
Using the above summary table, calculate the corrected AIC for each of the above
(c)
us a more reasonable preferred model) based on the data and number of predictors we are
considering?
Which of the AIC or the corrected AIC should be preferred (i.e. trusted to give
(d)
adjusted coefficient of determination for each of the models in (a). Based on this measure,
which model is preferred?
Now, knowing that the sample variance of gas mileage is 39.28 MPG, find the
(e)
model using each predictor as a response using the remaining predictors as predictors. Below
is a summary of each of these models.
Suppose we consider the smallest model (model 3 from part (a)). We can fit a
Response
Displacement
Horsepower
Weight
Predictors
Residual SE
Sample Variance of Response
Horsepower, Weight
Displacement, Weight
Displacement, Horsepower
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)?
Transcribed Image Text:An engineer is interested in finding a model that can explain the variation in gas mileage of cars (Y, in miles per gallon) using various characteristics of each vehicle model. The engineer has 11 vehicle characteristics to consider as possible predictors to build a multiple linear model: Engine Displace- ment, Horsepower, Torque, Compression ratio, Rear axle ratio, Carburetor, Number of transmission speeds, overall length, width, weight, and Type of transmission (automatic or manual). We can now consider a few different models and attempt to determine which model is better. (a) taken a sample of 30 vehicles, compute the AIC for each of the three models presented. Based on these values, which model would you say is better? Using the table of summary values below for 3 different models, and that we have Model Predictors included in each model Residual Standard Error all 11 predictors Displacement, Horsepower, Torque, Number of Transmission Speeds, Weight Model 1 3.227 Model 2 3.245 Model 3 Displacement, Horsepower, Weight 3.171 (b) models. Based on this, would we prefer the same model as in part (a)? Using the above summary table, calculate the corrected AIC for each of the above (c) us a more reasonable preferred model) based on the data and number of predictors we are considering? Which of the AIC or the corrected AIC should be preferred (i.e. trusted to give (d) adjusted coefficient of determination for each of the models in (a). Based on this measure, which model is preferred? Now, knowing that the sample variance of gas mileage is 39.28 MPG, find the (e) model using each predictor as a response using the remaining predictors as predictors. Below is a summary of each of these models. Suppose we consider the smallest model (model 3 from part (a)). We can fit a Response Displacement Horsepower Weight Predictors Residual SE Sample Variance of Response Horsepower, Weight Displacement, Weight Displacement, Horsepower 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)?
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