Several solution have been posted involving the following regression model: Test

Question

Several solution have been posted involving the following regression model: TestScore = 510 - 5.3*ClassSize, where 20.5 and 2.2 are the standard error of respective cooefficients, R^2 = 0.08 and the standard error of the regression is 12.0. But my question is a different: Suppose the TestScore variable was re-standardized by dividing by 100. In other words, TestScore2 = TestScore/100. What would be the new regression equation using TestScore2? What would be the new R^2 and standard errors of the coefficients and new regression model?

Explanation / Answer

regression coefficient is not independent of change of scale

here

TestScore = 510 - 5.3*ClassSize

(20.5) (2.2)

wjem Test Score is divided by 100 then each of coefficient and corresponding standard error will be changed as

TestScore = 510/100 - 5.3/100*ClassSize=5.1-0.053*ClassSize

(20.5/100) (2.2/100) = (0.205) (0.022)

in paranthesis it is standard error

R^2 will be unchanged as it will be 0.08 when TestScore will be divided by 100.

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