1. (30 points) Load the mtcars data in R. Consider mpg to be the response variable, and all other variables as features (a) Make a scatterplot matrix between mpg and all other features in the data. Additionally, compute the correlation coefficient between mpg and all other features in the dataset. (The two things can be done simultaneously with a single function.) What are the two features most strongly correlated with mpg? (Don't forget that correlation can be positive or negative so you should use the absolute value.) (b) Fit two simple linear regression models: Model 1 using the strongest features from (a) and model 2 using the second strongest feature from (a). Report the linear regression formula i.e., report the line equations) and the value of R from the two models. If you had to choose between these two models, which one would you choose and why? (c) Fit a multiple linear regression model with all features. Which features are significant in this model? What is the value of R in this models? (d) Using stepAIC identify the best subset of features. Fit a multiple linear regression model using the best subset of features. Write down the regression formula and R2 for this model. Are any of the features from (a) included in this model? Do they have the same coefficients as they had in model 1 or model 2 from (b)? If the coefficient values have changed, explain why 1. (30 points) Load the mtcars data in R. Consider mpg to be the response variable, and all other variables as features (a) Make a scatterplot matrix between mpg and all other features in the data. Additionally, compute the correlation coefficient between mpg and all other features in the dataset. (The two things can be done simultaneously with a single function.) What are the two features most strongly correlated with mpg? (Don't forget that correlation can be positive or negative so you should use the absolute value.) (b) Fit two simple linear regression models: Model 1 using the strongest features from (a) and model 2 using the second strongest feature from (a). Report the linear regression formula i.e., report the line equations) and the value of R from the two models. If you had to choose between these two models, which one would you choose and why? (c) Fit a multiple linear regression model with all features. Which features are significant in this model? What is the value of R in this models? (d) Using stepAIC identify the best subset of features. Fit a multiple linear regression model using the best subset of features. Write down the regression formula and R2 for this model. Are any of the features from (a) included in this model? Do they have the same coefficients as they had in model 1 or model 2 from (b)? If the coefficient values have changed, explain why