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Chapter 3: Q T3.3. (page 201)

The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is

(a) the correlation.

(b) the slope of the least-squares regression line.

(c) the square of the correlation coefficient.

(d) the intercept of the least-squares regression line.

(e) the residual.

Short Answer

Expert verified

The correct option is (c).

Step by step solution

01

Given information

The percentage of variation in y values explained by the least-squares regression of y on x

02

Concept

A regression line is a straight line that depicts the relationship between an explanatory variable xand a response variable y By entering any value of xinto the equation of the line, you may use a regression line to anticipate the value of y for any value ofx

03

Explanation

The coefficient of determination, or r2 is the percentage of variance in one variable explained by least-squares regression on the second variable. As a result, the square of the correlation coefficient is the fraction of the variance in Yvalues explained by the least-squares regression line of Yon X

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