Re-consider the expressions for calculating least squares coefficients for the s
ID: 3309443 • Letter: R
Question
Re-consider the expressions for calculating least squares coefficients for the slope b1 = r(Sy/Sx) and intercept b0 = y - b1x of a regression line. Use these formulas to explain what happens to the least squares line in the following situations.
(a) The mean value of the response variable increases, and all else remains the same, including
the standard deviations. [Hint: Report what happens to slope and to the intercept.]
(b) The mean value of the explanatory variable increases, and all else remains the same.
(c) The standard deviation of the values of the response variable increases, and all else remains
the same.
(d) The standard deviation of the values of the explanatory variable increases, and all else
remains the same.
(e) The correlation coefficient between the two variables moves closer to zero, and all else
remains the same.
Explanation / Answer
b1 = r * sy/sx , b0 = ybar - b1 * xbar
a) respnse variable = dependent = ybar increase , hence b0 increase , b1 same
b) xbar increases , b0 decrease , b1 decrease
c) sy increase hence b1 increase , b0 decrease
d) sx increase , hence b1 decrease , b0 increase
e) r decrease , hence hence b1 decrease , b0 increase
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