Business statistics

Question

Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as

y=−58.31x+93.97 and the r= −0.031.

What proportion of the variation in y can be explained by the variation in the values of x? 

r² = ______%

Report answer as a percentage accurate to one decimal place.

Answer 1

The coefficient of determination r^2 represents the proportion of the variation in the dependent variable y that can be explained by the independent variable x in a regression model.

In this case, r = -0.031, so r^2 can be calculated as follows:

r^2 = (-0.031)^2 = 0.000961

To express this as a percentage, multiply by 100:

r^2 = 0.000961* 100 = 0.0961

So, the proportion of the variation in y explained by the variation in x is approximately 0.0961%

Answer 2

Hi! I have answered the question in this video. I hope it helps. If you have any additional questions, please feel free to reach out to me! Take care,

Dr. Christal-Joy Turner