Report and interpret the R2 and the 2s associated with your best model

QMB 3200 FALL 2022 Project Submission 3

 

Complete your work in this document in black type. Leave the existing document in the blue type it is currently in and do not edit the document except to add your responses below each prompt. Submit to Canvas as a single doc or docx file; submissions consisting of multiple files or files submitted in inaccessible formats will not be graded. Check to make sure you submit the correct file; if you need to re-submit after the due date there will be a penalty of 25%. The assignment is due by November 18^th at 5:00pm; late work will be penalized 10% per day or portion of a day that it is late. This assignment is worth 45 points. You will use your student data set (cars) to run all analyses. NOTE: YOU MUST INCLUDE PRINTUTS IN ORDER FOR YOUR WORK TO BE GRADED. WITHOUT PRINTOUTS, YOUR GRADE WILL BE ZERO.

Refer to the video in Course Kaltura if you have any questions regarding how to correctly complete this assignment.

 

Delete one of your vehicle models from your data set, preferably the vehicle that was in the middle when you ranked your vehicle models by price in Project Submission 2. Recode the levels of Model Vehicle as 0 for one model and 1 for the other. We will no longer be using the variable “Year Manufactured” so you can delete that if you want. Add the quadratic term and the interaction terms. You will then start with the complete 2^nd-Order Model and “build down” through the entire model-testing process, until you have obtained the best-fitting model. Use this to respond to the following items. Refer to the video in Course Kaltura if you have any questions about what to do to your data set before you can begin your work.

Complete 2nd-Order Model: E(Y) = β₀ +β₁x₁ + β₂x₁² +β₃x₂ +β₄x₁x₂ + β₅x₁²x₂

 

Part 1: Model Building

 

A.1. Global F Test: run a test of the complete 2^nd order model. Insert the STATISTIX Printout of the results of this test. (3 points)

 

 

 

A.2  Fill in the following information for your Global F test (1 point per response/ total 5 points)

 

 

Test:    H₀:                                                       H_a:

 

Test Statistic:                                                  P-value:

 

Conclusion:

 

1. 1. Quadratics test: run a quadratics test. Insert the STATISTIX Printout of the results of this test. (3 points).

 

B.2. Fill in the following information for your quadratics test (1 point per response/ total     7 points)

 

Full Model:

 

Reduced Model:

 

Test:  H₀:                                                  H_a:

 

Test Statistic:                                          P-value:

 

Conclusion:

 

C.1. Interactions Test: run an interactions test. Insert the STATISTIX Printout of the results of this test. (3 points)

 

 

C.2.Fill in the following information for your interactions test (1 point per response/total 7 points)

 

Full Model:

 

Reduced Model:

 

Test:  H₀:                                                 H_a:

 

Test Statistic: ________________      P-value: ______________

 

Conclusion:

 

 

1. Would your model building be finished after the interaction test you ran in Part C.1.? Why or why not? (2 points)

 

 

 

Part 2: Final Model Interpretations

 

1. Identify the least squares prediction equation for your final model after all the testing was completed. You do not need to include the Printouts of any additional tests conducted, just the results of the best test. Use the values from the Printout and write the prediction equation below (use coefficient values, not betas). (3 points)

ŷ =

 

 

 

1. Report and interpret the R² and the 2s associated with your best model. (4 points)

 

1. Would you use your model in practice? Why or why not? (3 points)

 

 

Part 3: Using the model

 

1. Using your best model, predict the price and estimate the mean price for Case # 17 in your data set. Insert the STATISTIX Predicted and Fitted Intervals Printout of the results. (3 points)

 

 

1. Interpret the interval for the predicted value. (1 point)

 

1. Interpret the interval for the fitted value. (1 point)