Significant test for slope
The personnel director from electronics associates developed the following estimated regression equation relating an employee's score on a job satisfaction test to length of service and wage rate.
Y = 14.4 - 8.69x1 + 13.52x2
Where
x1 = length of service (years)
x2 = wage rate (dollars)
y = job satisfaction test score (higher score indicate greater job satisfaction)
A portion of the Minitab computer output follows. The regression equation is
Y = 14.4 - 8.69 X1 + 13.52 X2
|
Predictor
|
Coef
|
SE Coef
|
T
|
|
Constant
|
14.448
|
8.191
|
1.76
|
|
X1
|
|
1.555
|
|
|
X2
|
13.517
|
2.085
|
|
|
S = 3.773
|
R-sq = _____%
|
R - sq (adj) = _____%
|
Analysis of Variance
|
SOURCE
|
DF
|
SS
|
MS
|
F
|
|
Regression
|
2
|
|
|
|
|
Residual Error
|
|
71.17
|
|
|
|
Total
|
7
|
720.0
|
|
|
a. Complete the missing entries in this output (to 2 decimals).
Estimated Regression Equation
|
Predictor
|
Coefficient
|
SE Coefficient
|
T
|
|
Constant
|
14.448
|
8.191
|
1.76
|
|
X1
|
|
1.555
|
|
|
X2
|
13.517
|
2.085
|
|
R2_____ %
Analysis of Variance
|
Source
|
DF
|
SS
|
MS
|
F
|
|
Regression
|
2
|
|
324.415
|
22.79
|
|
Residual Error
|
5
|
71.17
|
14.234
|
|
|
Total
|
7
|
720.0
|
|
|
b. Using α = .05, is a significant relationship present?
c. Did estimated regression equation provide a good fit to the data?
d. Using the t test and α = .05 to test H0: β1 = 0 and β2 = 0
Compute the t test statistic for β1 (to 2 decimals).
What is the conclusion?
figure the t test statistic for β2 (to 2 decimals).
What is the conclusion?