Question

1. Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2 + β3 x3 + ε. Here, ε is the random error term that is assumed to be normally distributed with 0 mean and constant variance. State the estimated regression function. How are the estimates of the three regression coefficients interpreted here? Provide your output, and interpretations in a worksheet titled “Regression Output.”
2. Obtain the residuals and prepare a box-plot of the residuals. What information does this plot provide? Provide your output, and interpretations in a worksheet titled “Box Plots Residuals.”
3. Plot the residuals against the predicted value of y, x1, x2, and x3. Also prepare a normal probability plot. Interpret the plots and summarize your findings. Provide your output, and interpretations in a worksheet titled “Residuals Plots”
4. Calculate the Variance Inflation Factors for the model. Comment on the findings with respect to the multicollinearity assumption. Provide your output, and interpretations in a worksheet titled “Multicollinearity.”

y	x1	x2	x3
48	50	51	2.3
57	36	46	2.3
66	40	48	2.2
70	41	44	1.8
89	28	43	1.8
36	49	54	2.9
46	42	50	2.2
54	45	48	2.4
26	52	62	2.9
77	29	50	2.1
89	29	48	2.4
67	43	53	2.4
47	38	55	2.2
51	34	51	2.3
57	53	54	2.2
66	36	49	2
79	33	56	2.5
88	29	46	1.9
60	33	49	2.1
49	55	51	2.4
77	29	52	2.3
52	44	58	2.9
60	43	50	2.3
86	23	41	1.8
43	47	53	2.5
34	55	54	2.5
63	25	49	2
72	32	46	2.6
57	32	52	2.4
55	42	51	2.7
59	33	42	2
83	36	49	1.8
76	31	47	2
47	40	48	2.2
36	53	57	2.8
80	34	49	2.2
82	29	48	2.5
64	30	51	2.4
37	47	60	2.4
42	47	50	2.6
66	43	53	2.3
83	22	51	2
37	44	51	2.6
68	45	51	2.2
59	37	53	2.1
92	28	46	1.8

Answer 1