Part I: BMI data

The data for this part is contained in a file called 2050_F21_A3_BMI.csv. It is based on information from a sample of 200 males, and contains the following variables:

Body Mass Index (BMI). BMI =Weight in kg/(Height in metres)² . Waist to hip ratio (labelled WHR).

Bicep to forearm ratio (labelled BFR).

Age (years).

Import this data into R. (And look at the data after you've imported it!!!!) Run a multiple regression with BMI as the response variable and the other 3 variables as predictors. While there may be other meaningful predictors that could have been included, we will base our analysis on what is given in this data set. NB All interpretations, conclusions, etc. must relate to the practical problem at hand (i.e. must relate to the variables in this particular study).

1. Setting up the regression and interpreting some plots. a) Give the model equation for this multiple regression.

b) Give the R output for the multiple regression.

c) Plot the raw residuals against the predicted (fitted) values, a normal quantile-quantile plot of the raw residuals, and a scatterplot matrix of the response and predictors. Include these in your submission, Do these plots indicate any problems with the model? d) Plot partial regression plots for each of the predictors, and include them in your submission. Do any of these plots indicate a problem with the model, or suggest that we should use a different model? e) Which observation number has the largest leverage? Which observation number has the largest value of Cook's D? f) Plot the externally studentized residuals against the fitted values. What is the value of the most extreme studentized residual? Is it a major outlier worthy of concern?

Part II: BMI, continued

2. Conclusions and interpretations

a) Give a conclusion to the F test in the multiple regression R output.

b) Give an interpretation of the estimated slope of BFR.

c) Give an interpretation of the estimated slope of age.

d) Give a conclusion to the hypothesis test that the true slope of age is 0.

e) Give an interpretation of the estimated intercept in the R output. What sort of practical meaning does this have? f) Give an interpretation of the value of R2.

g) Using R's predict.lm function, find:

• i. a 95% confidence interval for the true mean BMI for 25 year old males with BFR = 1 and WHR = 0.9.
• ii. a 95% prediction interval for the BMI of a 25 year old male with BFR = 1 and WHR = 0.9.

BMI	WHR	BFR	AGE
25.91	0.91	1.07	33
30.21	1.1	1.15	72
25.85	0.97	1.14	62
21.21	0.81	1.08	31
24.85	0.9	1.05	43
31.84	1	1.16	66
26.35	0.84	1.23	27
26.21	0.9	1.18	46
21.79	0.95	1.06	40
26.4	0.95	1.17	43
31.84	0.94	1.18	26
26.21	0.9	1.15	26
27.04	1.04	1.04	72
26.84	0.94	1.09	56
27.45	0.95	1.19	49
29.04	0.94	1.01	28
30.32	1.03	1.18	67
25.57	0.98	1.16	24
23.02	0.96	1.17	81
19.08	0.86	1.13	39
23.31	0.9	1.09	61
24.55	1	1.14	70
23.37	0.84	1.2	43
30.45	0.99	1.15	28
29.35	0.98	1.22	62
26.08	0.97	1.03	64
23.98	0.95	1.16	48
20.33	0.87	1.06	34
21.07	0.88	1.01	42
26.77	0.91	1.14	47
26.34	0.97	1.12	46
23.59	0.91	1.05	25
22.64	0.88	1.03	64
32.29	1.06	1.13	44
24.77	0.91	1.08	35
22.85	0.89	1.07	68
27.39	0.96	1.18	35
23.08	0.85	1.12	40
25.89	0.93	1.04	49
25.01	0.92	1.03	54
24.57	0.89	1.14	40
21.96	0.86	1.18	24
27.43	0.92	1.13	42
24.58	0.91	1.16	72
22.89	0.94	1.1	31
23.42	0.87	1.07	47
29.73	0.97	1.09	34
22.04	0.88	1.11	43
24.78	0.89	1.05	38
21.33	0.94	1.2	55
21.32	0.89	1.08	54
23.79	0.85	1.13	29
26.22	0.93	1.11	44
23.93	0.89	1.14	42
23.12	0.89	1.14	42
19.85	0.93	1.08	34
24.68	1.04	1.13	72
30.33	0.94	1.12	35
23.6	0.9	1.07	48
22.26	0.79	1.02	42
25.89	0.9	1.1	50
31.98	0.99	1.07	49
21.57	0.84	1.08	43
28.11	0.91	1.08	35
28.34	0.95	1.13	42
23.32	0.84	0.97	27
28.2	0.87	1.22	28
21.95	0.83	1.06	27
23.96	0.9	1.11	47
26	0.99	1.11	43
25.64	0.91	1.18	43
20.65	0.84	0.96	35
24.28	0.91	1.1	40
21.41	0.89	1.07	49
23.67	0.87	1.13	44
28.49	0.94	1.17	30
23.98	0.87	1.14	43
37.67	1.08	1.19	51
29.84	1.01	1.12	74
23.67	0.94	1.04	49
26.65	0.99	1.19	49
23.06	0.9	1.14	40
26.35	1.02	1.21	43
22.92	0.86	1.09	61
29.74	1	1.17	41
23.22	0.8	1.11	28
25.53	0.97	1.11	44
25.2	0.93	1.09	35
23.35	0.9	1.16	40
25.45	0.94	1.05	46
20.35	0.85	0.77	30
27.41	0.94	1.09	50
32.25	1	1.18	41
26.12	0.99	1.07	43
22.39	0.84	1.09	27
18.06	0.82	1.13	40
24.29	0.9	1.14	36
26.17	0.92	1.07	53
23.27	0.88	0.97	48
21.67	0.89	1.17	42
25.97	1.01	1.19	52
26.79	0.97	1.1	55
30.69	0.9	1.14	26
19.27	0.83	1.02	25
25.13	0.99	1.08	67
24.42	0.93	1.08	27
20.61	0.86	1.02	40
30.92	1	1.18	65
23.21	0.94	1.13	40
24.39	0.99	1.09	60
27.11	0.96	1.13	41
31.03	0.95	1.69	36
27.26	0.94	1.12	44
28.02	0.95	1.23	39
25.45	0.91	1.15	56
21.56	0.82	1.12	23
25.64	0.94	1.14	55
21.87	0.87	1.11	55
20.78	0.91	1.15	65
24.94	0.85	1.1	26
27.98	0.98	1.14	41
24.83	0.97	1.15	50
23.15	0.89	1.11	42
29.9	0.95	1.12	25
28.5	1.09	1.1	54
20	0.89	1.15	55
22.24	0.84	1.14	29
20.61	0.86	1.07	39
23.37	0.88	1.11	35
27.65	0.97	1.17	58
21.07	0.92	1.14	51
31.2	0.97	1.23	48
27.27	0.91	1.07	28
24.33	0.93	1.12	51
26.94	0.99	1.07	44
21.39	0.86	1.12	32
21.6	0.9	1.01	55
21.72	0.95	1.05	54
20.64	0.83	1.06	40
26.69	0.97	1.2	69
25.27	0.94	1.12	40
29.11	1	1.23	72
24.16	0.98	1.21	43
29.55	0.97	1.14	57
24.63	0.89	1.13	28
22.91	0.91	1.14	47
27.94	1	1.16	61
26.21	0.95	1.09	52
25.37	0.91	1.11	55
29.08	0.95	1.15	40
25.33	0.98	1.16	64
22.81	0.82	1.16	54
22.48	0.87	1.08	41
25.2	0.95	1.07	58
27.36	0.92	1.18	34
25.33	0.95	1.05	35
25.87	0.97	1.17	47
26.12	0.95	1.15	27
33.25	0.97	1.17	37
20.16	0.81	1.04	47
23.39	0.88	1.09	47
24.19	0.9	1.04	58
29.29	0.99	1.17	61
24.43	0.93	1.07	31
26.09	1.02	1.15	62
23.61	0.94	1.06	48
24.76	0.92	1.23	40
25.63	0.92	1.15	52
22.53	0.83	1.09	26
22.84	0.91	1.07	50
31.97	1.02	1.19	63
21.61	0.84	1.19	51
24.54	0.89	1.14	41
28.38	0.96	1.16	55
30.55	0.98	1.15	69
29.22	0.98	1.14	41
30.54	0.93	1.19	41
27.59	1.03	1.09	54
33.96	1.03	1.16	65
20.38	0.92	1.13	45
23.41	0.92	1.19	64
22.07	0.83	1.07	23
29.96	1.04	1.1	67
22.71	0.91	1.11	40
29.79	1.01	1.19	42
23.97	0.91	1.06	41
23.03	0.91	1.06	49
23.64	0.85	1.12	26
23.69	0.87	1.03	46
19.71	0.8	1.06	27
24.08	0.96	1.16	57
26.51	0.88	1.17	24
26.46	0.94	1.12	42
20.82	0.86	1.09	56
27.51	0.91	1.15	38
27.62	0.92	1.23	33
21.36	0.88	1.01	47
27.6	0.94	1.61	44
21.34	0.85	1.16	28
21.34	0.89	1.15	37

You will be marked on: 1) Getting the proper R output and plots, 2) Validity of your statistical conclusions and interpretations, 3) Writing style (grammar and clear concise language count!), 4) Presentation (I'm not planning on being super picky on this point, but please make your submission easy to follow).

Note that you must use R.