Question

A sociologist was hired by a large city hospital 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 6 employees was chosen, and the following data were collected.
Distance to work (miles) 1 3 4 6 8 10
Number of days absent 8 5 8 7 6 3
a. Which variable is the independent variable?
Which variable is the dependent variable?
b. Develop the least squares estimated regression equation.
c. Predict the number of days absent for an employee that lives 5 miles from work.
d. Compute the coefficient of determination.
e. Compute the correlation coefficient.
f. Conduct a t-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
g. Conduct an F-test at a 0.05 level of significance to test for a significant relationship between
distance to work and number of days absent. State your conclusion.
h. Did you get the same conclusion for the t-test and the F-test? Will this always be the case for a
test for significance of the relationship in a simple linear regression?

Answer 1

a. Which variable is the independent variable?

The independent variable is Distance to work.
Which variable is the dependent variable?

The dependent variable is the Number of days absent.
b. Develop the least squares estimated regression equation.

y = 8.3193 - 0.4036*x
c. Predict the number of days absent for an employee that lives 5 miles from work.

y = 6.301
d. Compute the coefficient of determination.

r² = 0.479

	r²	0.479
	r	-0.692
	Std. Error	1.567
	n	6
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	9.0141	1	9.0141	3.67	.1278
Residual	9.8193	4	2.4548
Total	18.8333	5
Regression output				confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	8.3193
x	-0.4036	0.2106	-1.916	.1278	-0.9884	0.1812
Predicted values for: y
		95% Confidence Interval	95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
5	6.301	4.515	8.088	1.599	11.004	0.169

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