Question

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

Distance to Work (miles)	Number of Days Absent
1	8
3	5
4	8
6	7
8	6
10	3
12	5
14	2
14	4
18	2

Use Excel - no hand calculations.

1. Write the regression equation.

2. Interpret the regression constant and regression coefficient.

3. Forecast a value for the dependent variable, test the significance of the regression coefficient at an alpha level of .05

4. Test the overall significance of the regression model, and Interpret the coefficient of determination.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8431
R Square	0.7109
Adjusted R Square	0.6747
Standard Error	1.2894
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	32.6993	32.6993	19.6677	0.0022
Residual	8	13.3007	1.6626
Total	9	46.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8.098	0.8088	10.0119	0.0000	6.2327	9.9630
Distance to Work (miles) X	-0.3442	0.0776	-4.4348	0.0022	-0.5232	-0.1652

1. The regression equation is Y = a+bx
Y = 8.1-0.34X
Where Y is Number of Days Absent, X is Distance to Work (miles)

2. The regression constant is 8.1, means even when distance to work is zero, the average number of days employees absent is 8 days

The regression constant is -0.34, means with the increase in distance to work, the average number of days employees absent decreases. So for 1 mile increase in mile, the number of day employees absent decreases by -0.34

3. At a value of X =18, the value of Y = 8.1-0.34*18 = 1.98 or 2.
The regression coefficient is significant at alpha = 0.05 as the P-value of the coefficient is less than 0.05

4. The overall model is significant as the calculated F value is greater than significance F value in the ANOVA table Coefficient of determination or R^2 is 0.8431 which means the model is able to capture 84.31 percent of variation or Distance to work (miles) is able to explain the number of days absent by 84.31 percent