Question 3 Test of Equal Means – 4ptsA) State the Null and Alternative Hypotheses for the Test of Equal Means    B) What can you conclude from the ANOVA table with respect to the test of equal means at a significance level of 0.05 (FAIL TO REJECT or REJECT the null hypothesis)? Explain how you came to your conclusion.   C) Provide conclusions in the context of this problem.

Question 7 Confidence Intervals – 3ptsWhat are the bounds for a 99% confidence interval on the coefficient for Credit.Card.Debt?  Using this confidence interval, is the coefficient for Credit.Card.Debt plausibly equal to zero at this confidence level?  Explain.

Question 8 Residual Analysis – 10ptsPerform residual analysis on the lm.full model for the 4 assumptions. State whether the assumption holds and why you came to the conclusion.  

Question 12 – Predictions 4 – 3pts Using lm.full model, what is the predicted Car.Purchase.Amount and corresponding 90% prediction interval for a vehicle purchased in Mexico by a 45 year old female (0) with an annual salary of $65,000, Credit.Card.Debt of $2,000, and Net.Worth of $500,000?  Provide an interpretation of your results.  (Note: The data point has been provided. Ensure you are using lm.full not lm.red). 

Question 5 Exploratory Data Analysis Quantitative Variables – 4ptsNow consider the quantitative variables ONLY: Age, Annual.Salary, Credit.Card.Debt, and Net.Worth. Compute the correlation coefficients between each quantitative variables and also the response variable.  A) Which predicting variable has the best correlation with the response? B) Interpret the value of the best correlation coefficient in the context of the problem. Include strength (weak, moderate, strong) and direction (positive, negative).   C) Considering the predicting variables, does the correlation matrix show signs of multicollinearity? Explain how you came to your conclusion.

Submission Upload your knitted HTML file here.  Make sure to start submission of the exam 10 minutes before the end of the exam time. It is your responsibility to keep track of your time and submit before the time limit.  If you are unable to knit your file for whatever reason, you may upload your Rmd/ipynb file instead.  However, you will be penalized 5%. If you are unable to upload your exam file for whatever reason, you may IMMEDIATELY attach the file to the exam page as a comment via Grades-> Midterm Exam – Open Book Section (R) – Part 2 -> Comment box.  Note that you will be penalized 10% (or more) if the submission is made within 5 minutes after the exam time has expired and a higher penalty if more than 5 minutes. Furthermore, you will receive zero points if the submission is made after 15 minutes of the exam time expiring. We will not allow later submissions or re-taking of the exam. If you upload your file after the exam closes, let the instructors know via a private Piazza post. Please DON’T attach the exam file via a private Piazza post to the instructors since you could compromise the exam process. Any submission received via Piazza will not be considered.  

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.