INFERENTIAL STATISTICS

Certified BMW requires appropriate statistical analysis with a write up (memo) of approximately 3 pages.

1. a. Certified BMW thinks that the average price of all Model 330 cars is greater than $32,000.

Based on the sample data, is there evidence at the 5% level of significance that the average price of all Model 330 cars is greater than $32,000?

b. Clarify to Certified BMW which type of error (Type I or Type II) you might have made in your answer to 1(a).

c. Moving beyond the concept of a point estimate, provide an improved estimate of the average price of the Model 330 cars and explain why it is preferable to a point estimate.

2. Certified BMW would like you to further analyze your results.

a. Set up and test the hypothesis of whether the multiple regression model as a whole is significant. What is your conclusion at the 0.05 level of significance?

b. Test at the .05 level of significance to determine if there is an inverse relationship between price and mileage.

c. Test to determine if price is significantly different for the two types of BMW models. What is your conclusion at the 5% level of significance?

d. Are convertibles priced significantly higher than other cars? What is your conclusion at the 5% level of significance?

e. Do BMWs with manual transmissions (stick shift) sell for more or less than other cars? What is your conclusion at the 5% level of significance?

f. Use the regression equation to predict price for the first observation in the data set and calculate the residual.

g. Do you think that this regression model does a good job of predicting price? Why or why not?

h. Should Certified BMW be concerned about multicollinearity in this equation? Why or why not? If multicollinearity is a problem, how would you address it in this estimation?

3. a. Which estimate from Part II do you recommend Certified BMW use in estimating price: the one in question 1, the simple regression model's estimate in question 4, or the estimate based on the multiple regression in question 5? Justify your answer using the statistical results from Parts II and III.

b. Certified BMW thinks you can get a better estimate by adding additional independent variables to the equation. What criteria (not specific variables) would you suggest that they use to determine if a variable should be included? Propose at least one additional variable for this model that meets these criteria.

c. What statistical concern(s), if any, would you have in implementing your recommendation in this analysis? Explain your concern(s).

Attachment:- BMW Data.rar