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The coefficient of determination of a set of data points is 0.674. a. Can the li

ID: 3351602 • Letter: T

Question

The coefficient of determination of a set of data points is 0.674. a. Can the linear correlation coefficient be determined? If yes, obtain it. If no, why not? b. Can it be determined whether the slope of the regression line is positive or negative? Why or why not? c. If it is known that the slope of the regression line is negative, can the linear correlation coeficient be determined? If yes, obtain it. If no, why not? d. If it is known that the slope of the regression line is positive, can the linear correlation coefficient be determined? If yes, obtain it. If no, why not?

Explanation / Answer

SOlutionA:

Yes correlation coeff can be detrmined from Coefficient of determination

rsq=0.674

r=sqrT(0.674)

=0.820975

Solutionb:

we cannot tell that whether the slope is positive or negative.

as it is R sq

squared value

we cannot say its positive or negative.

Solutionc:

slope is linear correlation coefficient will be negative

b=slope

r=corr coeff

we can calculate r from slope as

b=r*Sy/Sx

slope is negative b=-

r=bSx/Sy

=-b Std deviation of X values/Std deviation of Y values

r will be negative value in this case.

yes linear correaltion coefficient can be determined

Solutiond:

from b=rSy/Sx

as slope is linear correlation coefficient is positive

r=b*Sx/Sy

yes linear correaltion coefficient can be determined