Question

15.9 For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock versus years with the firm.

x = 5 Years

    6
   12
   14
    6
    9
   13
   15
    9

y = 5 Shares

    300
    408
    560
    252
    288
    650
    630
    522

1. Determine the least-squares regression line and interpret its slope.

2. For an employee who has been with the firm 10 years, what is the predicted number of shares of stock owned?

For the data in Exercise 15.9, find the standard error of estimate, then construct the 95% prediction interval for the amount of stock owned by an individual employee who has been with the firm for 5 years.

Please construct the

1. The 95% confidence interval for x=10 for the average number of shares own for all the employees have 10 years of service with firm. 4 points

2. The 95% prediction interval for one employee who has 10 years service with the firm.4 points

Answer 1

Predicted number of shares of stock owned = 431.872

1.

95% Confidence Interval
lower	upper
351.817	511.927

2.

95% Prediction Interval
lower	upper
194.146	669.598

x	y
6	300
12	408
14	560
6	252
9	288
13	650
15	630
9	522
	r²	0.720
	r	0.849
	Std. Error	91.479
	n	8
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,29,173.128	1	1,29,173.128	15.44	.0077
Residual	50,210.372	6	8,368.395
Total	1,79,383.500	7
Regression output				confidence interval
variables	coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	44.3140
x	38.7558	9.8644	3.929	.0077	14.6184	62.8932
Predicted values for: y
		95% Confidence Interval	95% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
10	431.872	351.817	511.927	194.146	669.598	0.128