Question

9.13

Using the SHHS data in Table 2.10,fit all possible multiple regression models (without interactions) that predict the y variable serum total cholesterol from diastolic blood pressure,systolic blood pressure,alcohol,carbon monoxide and cotinine. Scrutinize your results to understand how the x variables act in conjuction.For these data,which is the "best " multiple regression model for cholesterol? What percentage of variation does it explain?

Serum total cholesrerol (mmol/l)	Diastolic blood pressure (mmHg)	Systolic blood pressure (mmHg)	Alcohol (g/day)	Cigarettes (no./day)	Carbon monoxide(ppm)	Cotinine (ng/ml)	CHD (1=yes,2=no)
5.75	80	121	5.4	0	6	13	2
6.76	83	139	64.6	0	4	3	2
6.47	76	113	21.5	20	21	284	2
7.11	79	124	8.2	40	57	395	2
5.42	100	127	24.4	20	29	283	2
7.04	79	148	13.6	0	3	0	2
5.75	79	124	54.6	0	3	1	2
7.14	100	127	6.2	0	1	0	2
6.1	79	138	0	0	1	3	2
6.55	85	133	2.4	0	2	0	2
6.29	92	141	0	0	7	0	2
5.98	100	183	21.5	20	55	245	1
5.71	78	119	50.2	0	14	424	2
6.89	90	143	16.7	0	4	0	1
4.9	85	132	40.6	4	7	82	2
6.23	88	139	16.7	25	24	324	2
7.71	109	154	7.2	1	3	11	1
5.73	93	136	10.8	0	2	0	1
6.54	100	149	26	0	3	0	2
7.16	73	107	2.9	25	29	315	1
6.13	92	132	23.9	0	2	2	2
6.25	87	123	31.1	0	7	10	2
5.19	97	141	12	0	3	4	1
6.05	74	118	23.9	0	3	0	2
7.12	85	133	24.4	0	2	0	2
5.71	88	121	45.4	0	8	2	2
6.19	69	129	24.8	15	40	367	1
6.73	98	129	52.6	15	21	233	2
5.34	70	123	38.3	1	2	7	2
4.79	82	127	23.9	0	2	1	2
6.78	74	104	4.8	0	4	7	2
6.1	88	123	86.1	0	3	1	1
4.35	88	128	15.5	20	11	554	2
7.1	79	136	7.4	10	9	189	1
5.85	102	150	4.1	0	6	0	2
6.74	68	109	1.2	15	15	230	2
7.55	80	135	92.1	25	29	472	2
7.86	78	131	23.9	6	55	407	1
6.92	101	137	2.5	0	3	0	2
6.64	97	139	119.6	40	16	298	2
6.46	76	142	62.2	40	31	404	1
5.99	73	108	0	0	2	4	2
5.39	77	112	11	30	11	251	2
6.35	81	133	16.2	0	3	0	2
5.86	88	147	88.5	0	3	0	2
5.64	65	111	0	20	16	271	2
6.6	102	149	65.8	0	3	1	2
6.76	75	140	12.4	0	2	0	2
5.51	75	125	0	25	16	441	2
7.15	92	131	31.1	20	36	434	1

Answer 1

Here I try to fit a multiple linear regression model using spss. I have seen that none of the variables are significant. Due to this the R squared value is very low . Only 14.5% of the total variation can be explained by the proposed model.  I am attatching the model summary here.

But the model satisfies all the assumptions for the multiple linear regression model. I attaching that also

From the table it is clear that there is no multicollinearity in the data.

the residuals are normal also.