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Why does decreasing the SD of the Independent Variable in a linear regression model increase the...

Why does decreasing the SD of the Independent Variable in a linear regression model increase the sample sizs?
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Answer #1

Lnear Regression Model is given by:

,

where

x is the Independent Varriable,

y is the Dependent Variable

is the y ietercept

is the slope

The SD of the Independent Variable is given by:

.            (1)

where

is the mean of yvalues and n is the sample size.

So,

Answer is:

if we decrease the SD of the Independent Variable, we note that since n = the sample sizs occurs in the demominator, the sample size = n increases.

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