Question

Consider the following regression output where the dependent variable is testscores and the two explanatory variables are the student-teacher ratio and the percent of English learners:

TestScore = 698.9 - 1.10 x STR - 0.650 x PctEL.
You are told that the t-statistic on the student-teacher ratio coefficient is 2.56.
1. The standard error therefore is approximately ____________.
A) 0.43
B) 0.650
C) 0.25
D) 1.96

Answer 1

The correct option is (A).

Explanation:

The multiple linear regression equation is given by,
`y=\alpha +\beta _(1) x_(1)+\beta _(2)x_(2)`, where α = constant and β
`_(i)` = slope coefficients of regression line.

To test if there is a important relationship amid X
`_(i)` and Y, we use the t-statistic test.

The t-statistic for regression coefficient analysis is given by,

`t=\frac{\beta_(i)}{S.E._{\beta_(i)}}`

The regression equation for test scores dependent upon the two explanatory variables, the student-teacher ratio and the percent of English learners is:

`\text{TestScore} = 698.9 - 1.10 \text{ STR} - 0.650 \text{ PctEL}`

A t-test for the significance of the regression coefficient of variable student-teacher ratio (STR) is conducted.

The test statistic is found to be, t = 2.56.

The regression coefficient of variable STR is, 1.10.

Compute the standard error of the regression coefficient as follows:

`t=\frac{\beta_(i)}{S.E._{\beta_(i)}}`

`S.E._{\beta_(i)}=(\beta_(i))/(t)`

`=(1.10)/(2.56)\\\\=0.4296875\\\\\approx 0.43`

The standard error of the regression coefficient is 0.43.

Thus, the correct option is (A).