Question

Suppose that the measurements of arm span and height were converted from centimeters to meters by dividing each measurement by 100. How will this conversion affect the values of r2 and s?

a. r2 will increase, s will increase.

b. r2 will increase, s will stay the same.

c. r2 will increase, s will decrease.

d. r2 will stay the same, s will stay the same.

e. r2 will stay the same, s will decrease.

Short answer

The correct option is (e)$r^2$will stay the same, $s$will decrease.

Step-by-step solution

Given information

The regression equation is:$\stackrel{⏜}{y}=6.4+0.93x$

Explanation

The coefficient of determination reveals how much variance in the response variable is explained by the predictor variable. The relationship between the variables is unaffected by the change in unit. Because there is no change in the relationship. As a result, the coefficient of determination will remain unchanged. The sample size has a negative relationship with the standard deviation. The s would be reduced by dividing by $100$ As a result, the residual's standard deviation would decrease. Hence, the correct option is (e).