SOLUTION: 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=-23.98

Algebra ->  Probability-and-statistics -> SOLUTION: 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=-23.98      Log On


   

Question 1089000: 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=-23.98x + 55.52 and the r=-0.438.
What proportion of the variation in y can be explained by the variation in the values of x?
rē = ? %
Report answer as a percentage accurate to one decimal place.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
r^2 = (-.438)^2 = .191844

approximately 19.2% of the variation in y can be explained by the variation in x.

excerpt from http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.
The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:
R-squared = Explained variation / Total variation
R-squared is always between 0 and 100%:
0% indicates that the model explains none of the variability of the response data around its mean.
100% indicates that the model explains all the variability of the response data around its mean.
In general, the higher the R-squared, the better the model fits your data.