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MTH303 Coursework Fall 2022 (Total 250pts)

Question 1 (100 pts)

Step 1 (10 pts) Load CockpitNoise.xlsx

Step 2 (10 pts) Generate a correlation matrix among predictor variables.

Step 3 (10 pts) Compute the critical value  to test the following hypothesis test of zero correlation (use level of significance 5%):

and compute , where  is the number of samples.

Step 4 (10 pts) Highlight cells if the null hypothesis of zero correlation at Step 3 is rejected. Do not highlight cells if the null hypothesis is not rejected.

Can you find multicollinearity? Justify your answer.

Step 5 (10 pts) Perform backward stepwise linear regression. You should show AIC at every step and plot it with respect to step number (an example plot is at the below).

Step 6 (10 pts) Print estimated coefficients with standard error, t-value, and p-value of the final model from Step5.

Step 7 (10 pts) Compute variance inflation factor (VIF) for the predictor variables of the final model from Step5.

(10 pts) Can you find multicollinearity in your model? Justify your answer by using VIF. If yes, should we remove the predictor variables with high VIF?

Step 8 Check the following assumptions of residuals for your final linear regression model. Justify your answer for each assumption.

Assumption 1 (5 pts): The errors are normally distributed.

Assumption 2 (5 pts): The errors have constant variance.

Assumption 3 (10 pts): The errors are independent. 

Question 2 (150 pts)

A survey is carried out to study the effect of computer programming experience on ability to complete a complex programming task within a given period. Thirty persons with different programming experience (measured in months) were selected to solve the same programming problem. Their personal information and the results of their success in the task are shown in Table below, where Y=1 if the task was completed, and Y=0 if the task was not completed; X₁=1 if the person is male and X₁=0 if the person is female.

A. Carry out a logistic regression (using the logit link function) to study whether gender and experience have effects on the completion of the task. You need to simplify the model based on ANCOVA; report the final model you selected and make a conclusion on it; carry out a residual analysis and comment on it.                                               (60 pts)

B. Based on the model used in A, predict the probability that a male with 20 months of experience can complete the task on time.                                                                   (20 pts)

C. Repeat A by using probit link function. Among models using logit and probit link functions, find the best one among them and claim your reason.                            (20 pts)                    

D. Use Poisson regression with canonical link function to build a model for Months of Experience (X₂) and Gender (X₁). Determine whether male and female have significant difference in mean experience, and provide a 95% confidence interval for the ratio (male’s experience/female’s experience) of two means.                                          (50 pts)