The proportion of the variation in the values of a response y that is explained
ID: 3242176 • Letter: T
Question
The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is the
A) correlation coefficient. B) square of the correlation coefficient. C) slope of the least-squares regression line. D) intercept of the least-squares regression line.
Which of the following is correct? The mean of the residuals from least-squares regression is 0. The square of the correlation is the proportion of the data lying on the least-squares regression line. The correlation r is the slope of the least-squares regression line. The square of the correlation is the slope of the least-squares regression line.Explanation / Answer
1. Correct Answer: Option (B) square of the correlation coefficient
Since,
It is also called correlation determination. In regression, the correlation determination R2 , is a statistical measure of how well the regression lineapproximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data. It measures the percentage of variation in the variable Y can be exlained by the indepedent variable X
2. Correct Answer: Option (A) The mean of the residuals from least-squares regression is 0.
since sum of the residuals are equal to zero, so mean of the residuals is also zero
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