Question

You have estimated the relationship between test scores and the student-teacher ratiounder the assumption of homoskedasticity of the error terms. The regression output is asfollows: ^TestScore = 698.9 - 2.28x STR, and the standard error on the slope is 0.48. Thehomoskedasticity-only “overall” regression F- statistic for the hypothesis that theRegression R2 is zero is approximatelya. 0.96b. 1.96c. 22.56d. 4.75

Answer 1

The correct option is c.

Explanation:

The given regression output is

`\widehat{Test Score}=698.9-2.28* STR` ... (1)

The standard error on the slope is 0.48.

The slope intercept form of regression line is

`Y=B_0+B_1x` .... (2)

The test statistic is a t statistic (t) defined by the following equation.

`t=(B_1)/(SE)` ... (3)

From (1) and (2) we get

`B_0=698.9,B_1=-2.28`

Substitute
`B_1=-2.28` and SE=0.48 in equation (3).

`t=(-2.28)/(0.48)`

`t=-4.75`

So, the F-statistics is

`F-statistics = t^2`

`F-statistics = (-4.75)^2`

`F-statistics =22.56`

Therefore the correct option is c.