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

Question

A.Develop the least squares estimated regression equation (to 3 decimals).
Days Absent =_____ +_____ Distance

B. 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 - Select your answer

1.less than .01

2.between .01 and .025

3.between .025 and .05

4.between .05 and .10

5. greater than .10

What is your conclusion?
1.Conclude that there is a significant relationship between days missed and distance from work

2. Do not conclude that there is a significant relationship between days missed and distance from work

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).

(_____, _____)

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 10 12 14 14 18 a. Which of the following scatter diagrams accurately represents these data?

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Days Absent
Independent Variable: Distance
Days Absent = 7.1955455 - 0.32918082 Distance
Sample size: 10
R (correlation coefficient) = -0.79340162
R-sq = 0.62948614
Estimate of error standard deviation: 1.4532478

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

A) Days absent = 7.196 + (-0.329) Distance

B) F = 13.59

p - value is less than 0.01

Conclude that there is a significant relationship between days missed and distance from work

r2 = 0.629

95% CI: (4.2, 6.9)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 7.1955455 0.93348805 0 8 7.7082353 <0.0001 Slope -0.32918082 0.089289148 0 8 -3.6866834 0.0062

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