Car Purchasing Data Analysis For this exam, you will be building a model to predict car purchase prices (Car.Purchase.Amount) that are sold in different countries of Mexico, Canada, and USA. The “Car_Purchasing_Data.csv” data set consists of the following variables: Country: country in which the car is sold (3-letter identifier) Gender: gender of the buyer (0=female, 1=male) Age: age of the buyer (years) Annual.Salary: annual salary earned of the buyer ($ USD) Credit.Card.Debt: amount of reported credit debt owed by buyer ($ USD) Net.Worth: amount of reported assets of buyer ($ USD) Car.Purchase.Amount: amount the car was purchased for by buyer ($ USD) Read the data and answer the questions below. Assume a significance threshold of 0.05 for hypothesis tests unless stated otherwise. # Read the data setbuyers = read.csv(‘Car_Purchasing_Data.csv’, header=TRUE)#Set Gender & Country as a categorical variablebuyers$Gender

Question 11 – Reduced Model 6ptsCreate a third model called lm.red by removing Credit.Card.Debt and Gender from lm.full. Display the summary.   A) Comment on the removal of the predicting variables by comparing lm.red to the full model (lm.full).  Note any changes to the statistical significance of the coefficients.   B) Perform a partial F-test on the new model (lm.red) vs the previous model (lm.full), using alpha=0.05.  Do you reject or fail to reject the null hypothesis?  Explain your answer using the output.   C) Do the variables Credit.Card.Debt and Gender add predictive power?  (Yes or No should suffice in conjunction w/ 11B)

Question 10 – Outlier Detection – 3 ptsUsing Cook’s distances, evaluate whether there are any outliers in the lm.full model. Display your plot and state your conclusion. (Note: Do not remove any observations)

Question 1 – Exploratory Data Analysis of Categorical Variable – 2ptsCreate a boxplot of the response variable Car.Purchase.Amount and the categorical variable Country. From this plot, does Country appear useful in predicting Car.Purchase.Amount?  Explain how you came to your conclusion.

What is the value of C, the degrees of freedom of the F-statistic?

If is not invertible, then the columns of are not linearly independent and hence, multicollinearity exists, although we can still estimate

Suppose that we have a multiple linear regression model with quantitative predictors, one qualitative predictor with categories and an intercept. Consider the estimated variance of the error terms based on observations. The estimator should follow a Chi-square distribution with

Multiple regression analysis is used when:

A dataset on traffic congestion on several bridges crossing the same river contains 1098 data points and 4 bridges.  What are the degrees of freedom of the F-test when comparing treatments using ANOVA?

What is the value of A, the t-value for Wine_Consumption_per_capita?