Assignment #6: Regression Homework 1 DUE 6 February 2020 SECTION A: Podcast ***NOTE: DO PART 1 BELOW BEFORE LISTENING TO THE PODCAST*** Part 1: (1 pt) Below is a screen shot of an actual tweet from...

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Assignment #6: Regression Homework 1 DUE 6 February 2020 SECTION A: Podcast ***NOTE: DO PART 1 BELOW BEFORE LISTENING TO THE PODCAST*** Part 1: (1 pt) Below is a screen shot of an actual tweet from @DataIsBeautiful from August 2016. X-Axis: Average household income for the particular zip code/city that this data comes from Y-Axis: Average # of traffic tickets issued per person in the zip code/city 1. What message do you think @DataIsBeautiful is trying to convey with this graph? Part 2: (9 pts) Listen to the podcast on Heteroskedasticity from Data Skeptic. 1. In reference to the tweet above, the (male) podcaster discusses Hyman’s Categorical Imperative which states that before investigating if a phenomena is true, you need to first establish that the phenomena exists. He uses this as a basis for a key problem that he has with the above graph. Which assumption of the model does he have an issue with (i.e. - what does he question the existence of in this case)? (2 pts) 2. As discussed in class, the examination of the residuals plot is important for testing the models assumptions for linearity and constant variance (homoscedasticity). a. Do a rough sketch of what you think the residual plot would look like for the above model. (3 pts) Residuals 0 Prediction b. What does this tell you about the model’s prediction for i. Incomes < $40,000="" (1="" pt)="" ii.="" $65,000="">< incomes="">< $85,000="" (1="" pt)="" iii.="" incomes=""> $85,000 (1 pt) c. What does this tell you about the homoscedasticity of the model? (1 pt) SECTION B: Regression Analysis (30 pts) For this part of the assignment, I would like you to develop a predictive model for body mass using a number of body measurements (all in cm) using JMP. (Use Physical.jmp) There are 22 observations across 10 variables. The variables are: 1. MassWeight in kg 2. ForeMaximum circumference of forearm 3. BicepMaximum circumference of bicep 4. ChestDistance around chest directly under the armpits 5. NeckDistance around neck, approximately halfway up 6. WaistDistance around waist, approximately trouser line 7. ThighCircumference of thigh, measured halfway between the knee and the top of the leg 8. CalfMaximum circumference of calf 9. HeightHeight from top to toe 10. ShouldersDistance around shoulders, measured around the peak of the shoulder blades Part 1 – Test Multicollinearity 1. How many pairs of variables have potential multicollinearity issues? (greater than 0.50) (2 pts) 2. Which two variables seem to have the least issues with multicollinearity? (1 pt) Part 2 – Run a multiple regression model using the “all-in” method of Standard Least Squares 1. How much variability in our dependent variable is explained by the independent variables? (1 pt) 2. Is the Regression Significant? _______________ What is its p-value? _____________ (2 pts) 3. How many variables are significant? List them and explain how you came to that conclusion. (2 pts) 4. Are there any variables which have potentially significant variance inflation problems? List them and explain how you came to that conclusion. (2 pts) Part 3 – Using Backward Stepwise Regression, develop a predictive model for body mass using JMP 1. List the variables removed from your model and the order in which they were removed. (3 pts) 2. How did you decide to which variables to remove? (1 pt) 3. In your final model a. How many independent variables remain? (1 pt) b. Which independent variable is relatively the most important to the model? Least important? (2 pts) c. Do any of the variables have any potential multicollinearity issues? Support your conclusion. (1 pt) d. How much variability in our dependent variable is explained by the independent variables? (1 pt) e. What is your regression equation? (round coefficients to 2 decimal places) (1 pt) 4. What is your prediction for a person with the following measurements: (2 pts) a. Forearm: 29.5 cm b. Bicep: 36.5 cm c. Chest: 105 cm d. Neck: 36.5 cm e. Shoulder: 105 cm f. Waist: 93 cm g. Height: 183.5 cm h. Calf: 38 cm i. Thigh: 52 cm j. Head: 58 cm Part 4 – Test the model assumptions for your final model in Part 3 1. We discussed a 4 assumption in class, one does not need to be tested in this case. Which one and why? (2 pts) 2. Test the 3 remaining assumptions and support your decision as to whether the assumptions are upheld by this model. (6 pts) 2