Question

The following data gives the creatinine clearance Y (in $1000’s) of a sample of 33 male subjects along with their creatinine concentration (X1), age (X2) and the weight (X3). The data are:

X1	X2	X3	Y
0.71	38	71	132
1.48	78	69	53
2.21	69	85	50
1.43	70	100	82
0.68	45	59	110
0.76	65	73	100
1.12	76	63	68
0.92	61	81	92
1.55	68	74	60
0.94	64	87	94
1.07	49	93	98
0.70	43	60	112
0.71	42	70	125
1.0	66	83	108
2.52	78	70	30
1.13	35	73	111
1.12	34	85	130
1.38	35	68	94
1.12	16	65	130
0.97	54	53	59
1.61	73	50	38
1.58	66	74	65
1.40	31	67	85
0.68	32	80	140
1.20	21	67	80
2.10	73	72	43
1.36	78	67	75
1.50	58	60	41
0.82	62	107	120
1.53	70	75	52
1.58	63	62	73
1.37	68	52	57

1. Plot a scatter plot of Y against each predictor variable. What do the plots tell you about the nature of the relationship between y and each of the independent variables?
2. Obtain the correlation matrix of the X variables. Does the matrix indicate potential problems with multicollinearity?
3. Fit a regression model containing the independent variables as first order terms.
4. Obtain variance inflation factors for the model in (. Is multicollinearity a problem? Explain
5. Obtain residual plots as well as partial residual plots. Do these plots indicate that the regression model should be modified?
6. Theoretical considerations .suggest the model

E(ln(Y)) = b₀+ b₁ln(X₁)+ b₂ln(140-X₂)+b₃ln(X₃).

Fit the theoretical model and examine all the relevant model diagnostics. Do any of the problems encountered with the model in (d) (if there were any problem encountered) seem to have been resolved?

Answer 1