Question

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

a. Regression eq: y=43.801+38.81X, where x=the number of years with the firm
b. The standard error of estimate S_y,x=91.48.

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

First i have fit the model by using R software

x=c(6,12,14,6,9,13,15,9)
> x
[1] 6 12 14 6 9 13 15 9
> y=c(300,408,560,252,288,650,630,522)
> y
[1] 300 408 560 252 288 650 630 522

> model=lm(y~x)
> model

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
44.31 38.76

> summary(model)

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-105.12 -45.52 -10.25 42.83 128.88

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 44.314 108.509 0.408 0.69716   
x 38.756 9.864 3.929 0.00772 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 91.48 on 6 degrees of freedom
Multiple R-squared: 0.7201, Adjusted R-squared: 0.6734
F-statistic: 15.44 on 1 and 6 DF, p-value: 0.007723