Effect of Rescaling on Regression Slope
A study on the effect of the number of close friends, x, on evening Facebook checks, y, produced the least-squares regression equation $\hat{y} = -1.73 + 0.5492x$. If the x variable is rescaled by multiplying all of its values by 10, a researcher claims the slope of the new regression line will still be 0.5492. Which statement best explains the researcher’s error?
They mistakenly assumed that the correlation coefficient is affected by scaling, when it should remain unchanged.
They overlooked that scaling the predictor variable changes its standard deviation, which in turn alters the slope; the new slope should be 0.5492 divided by 10.
No mistake was made; the regression slope is invariant under rescaling of the predictor variable.
They inverted the regression equation, so actually the intercept would change instead of the slope.
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