Question

Suppose that a health researcher is interested in determining whether the distance between the patient’s residence and source of care, and # of disability days significantly predict the number of visits at a local hospital.

Visits	Distance	Disability days
7	1	8
7	1	9
2	10	1
4	4	3
5	2	5
3	9	2
2	10	1
9	2	10
6	3	7
2	11	2
4	2	3
7	2	8
3	14	2
2	16	1
8	2	9
4	4	2
6	2	5

a. Determine the multiple regression equation for the data and interpret the regression coefficients.

b. Provide an interpretation of the coefficient of multiple determination, R2.

c. At the 5% significance level, determine if # of disability days and distance between patient’s residence and source of care significantly predict the number of visits.

Answer 1

a. Determine the multiple regression equation for the data and interpret the regression coefficients.

First arrange data in Excel as,

Visits	Distance	Disability days
7	1	8
7	1	9
2	10	1
4	4	3
5	2	5
3	9	2
2	10	1
9	2	10
6	3	7
2	11	2
4	2	3
7	2	8
3	14	2
2	16	1
8	2	9
4	4	2
6	2	5

To determine the multiple regression using excel data analysis tool as below,

The Output of Regression is,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.980
R Square	0.960
Adjusted R Square	0.954
Standard Error	0.496
Observations	17
ANOVA
	df	SS	MS	F	Significance F
Regression	2	81.615	40.808	165.911	0.000
Residual	14	3.443	0.246
Total	16	85.059
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.469	0.469	5.262	0.000	1.463	3.475
Distance	-0.081	0.038	-2.104	0.054	-0.163	0.002
Disability days	0.599	0.059	10.229	0.000	0.473	0.724

b. Provide an interpretation of the coefficient of multiple determination, R2.

As we can see in output,

R2 = 0.960 i.e 96%

The model explains 96% the variability of the response data Visit.

c. At the 5% significance level, determine if # of disability days and distance between patient’s residence and source of care significantly predict the number of visits.

As we can see in output,

distance

P-value of Distance is 0.054, is greater than 0.05 Then, distance variable Insignificantly predict.

Disability days,

P-value of Distance is 0.000, is less than 0.05 Then, Disability Days variable significantly predict.the number of visits.