Question

A hospital administration wished to study the relation between patient satisfaction (Y) and patient’s age (X1), severity of illness (X2) and anxiety level. The administration randomly selected 15 patients and the results of the study are shown below.

 

The regression equation is

y = 184 - 0.976 x1 - 1.14 x2 - 12.3 x3

 

 

Predictor     Coef  SE Coef      T

Constant    184.02    31.70   5.81  

x1         -0.9763   0.4500  -2.17  

x2         -1.1361   0.9786  -1.16  

x3          -12.34    14.30  -0.86  

 

 

S = 11.0529   R-Sq = 70.2%   R-Sq(adj) = 62.0%

 

 

Analysis of Variance

 

Source          DF      SS      MS     F

Regression       3  3161.5  1053.8  8.63

Residual Error  11  1343.8   122.2

Total           14  4505.3

 

 

Obs	Y	X1	X2	X3	residual	d	r	Hii	COOK	DFFIT
1	48	50	51	2.3	-0.88	-0.09	-0.09	0.20	0.00	-0.04
2	57	36	46	2.3	-11.23	-1.14	-1.15	0.20	0.08	-0.58
3	66	40	48	2.3	3.95	0.38	0.36	0.11	0.00	0.13
4	70	41	44	1.8	-1.79	-0.20	-0.19	0.37	0.01	-0.15
5	89	28	43	1.8	3.38	0.37	0.35	0.30	0.01	0.23
6	36	49	54	2.9	-3.05	-0.36	-0.35	0.43	0.02	-0.30
7	46	42	50	2.2	-13.06	-1.24	-1.27	0.09	0.04	-0.39
8	54	45	48	2.4	-1.94	-0.20	-0.19	0.22	0.00	-0.10
9	26	52	62	2.9	-1.03	-0.13	-0.12	0.49	0.00	-0.12
10	77	29	50	2.1	4.01	0.43	0.42	0.29	0.02	0.27
11	89	29	48	2.4	17.44	1.93	2.26	0.33	0.45	DFFIT11
12	67	43	53	2.4	14.79	1.40	1.47	0.09	0.05	0.46
13	47	38	55	2.2	-10.29	-1.15	-1.17	0.35	0.18	-0.86
14	51	34	51	2.3	-13.50	-1.33	-1.38	0.15	0.08	-0.58
15	57	53	54	2.2	13.22	1.53	1.64	0.39	0.37	1.30

 

 

 

 

 

Answer the following questions.

 

a) Name 3 methods of scaling residuals.      (3 marks)

 

b) Name 2 method to measures of influential.     (2 marks)

 

c) Obtain the full model for the above problem.     (1 mark)

 

d) Test the multiple regression model for significance at the 0.05 level. (5 marks)

 

e) From the standardized residual, identify any outlier.    (2 marks)

 

f) From the hat matrix, identify any leverage.     (2 marks)

 

g) Calculate the value of DFFITS.      (4 marks)

 

h) Comment on the value in (g) in term of influence.    (1 mark)

 

 

Answer 1