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 10 employees was chosen, and the following data were collected. Distance to Work Number of Days Absent 2 9 4 6 4 9 7 8 9 7 11 4 13 7 15 3 15 6 19 3 Which of the following scatter diagrams accurately represents these data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 Develop the least squares estimated regression equation (to 3 decimals). Days Absent = + Distance Is there a significant relationship between the two variables? Use = .05. Compute the value of the F test statistic (to 2 decimals). The p-value is What is your conclusion? What is the value of r2 (to 3 decimals)? Note: report r2 between 0 and 1. Did the estimated regression equation provide a good fit? Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal). ( , )

Answer 1

Result:

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 10 employees was chosen, and the following data were collected. Distance to Work Number of Days Absent 2 9 4 6 4 9 7 8 9 7 11 4 13 7 15 3 15 6 19 3 Which of the following scatter diagrams accurately represents these data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3

Develop the least squares estimated regression equation (to 3 decimals).

Days Absent =9.299   -0.313 *Distance

Is there a significant relationship between the two variables? Use = .05. Compute the value of the F test statistic (to 2 decimals). The p-value is

F=12.85, P=0.0071

What is your conclusion?

The regression is significant. There is a significant relationship between the two variables.

What is the value of r2 (to 3 decimals)? 0.616

Note: report r2 between 0 and 1. Did the estimated regression equation provide a good fit?

Yes, estimated regression equation is provide a good fit.

Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal). ( , )

95% CI =(6.3, 9.2)

Regression Analysis
	r²	0.616	n	10
	r	-0.785	k	1
	Std. Error	1.479	Dep. Var.	NumberofDaysAbsent
ANOVA table
Source	SS	df	MS	F	p-value
Regression	28.1075	1	28.1075	12.85	.0071
Residual	17.4925	8	2.1866
Total	45.6000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	9.2987	0.9827	9.463	1.28E-05	7.0327	11.5647
DistancetoWork	-0.3130	0.0873	-3.585	.0071	-0.5143	-0.1117
Predicted values for: NumberofDaysAbsent
		95% Confidence Interval		95% Prediction Interval
DistancetoWork	Predicted	lower	upper	lower	upper	Leverage
5	7.734	6.272	9.195	4.024	11.444	0.184