Question

Exhibit 15-6
Below you are given a partial computer output based on a sample of 16 observations.

	Coefficient		Standard Error
Constant	12.924		4.425
X1	-3.682		2.630
X2	45.216		12.560
Analysis of Variance
Source of Variation	Degrees of Freedom		Sum of Squares	Mean Square	F
Regression			4,853	2,426.5
Error				485.3

Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Group of answer choices

3.41

3.63

3.81

19.41

Answer 1

To test if there is a relationship among the variables,

The test statistic can be written as

F statistic = Mean square(Regression) / Mean square(Error) ,

which under H0 follows a F distribution with df = (df(Regression), df(Error) )

So,

The value of F statistic is

df(Regression) = 2 (since there are two predictors X1 and X2 )

df(Error) = number of observations - df(Regression) = 16 - 2 = 14

At 5% level of signiifcance,

critical F value =