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  8.69x_{1} + 13.52x_{2}
Where
x_{1} = length of service (years)
x_{2} = 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

Rsq = _____%

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


R^{2}_____ %
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 H_{0}: β_{1} = 0 and β_{2} = 0
Compute the t test statistic for β_{1} (to 2 decimals).
What is the conclusion?
figure the t test statistic for β_{2} (to 2 decimals).
What is the conclusion?