Imagine that the linear correlation between variables X and Y is r = 0.35. Further imagine...
Imagine that the linear correlation between variables X and Y is r = 0.35. Further imagine that the mean of variable X is 4 and that the mean of variable Y is 6. If we correctly calculated a simple linear regression equation to predict values of Y (based on the corresponding value of X), how much error could we remove from our predictions, relative to just guessing the mean of Y = 6 for everyone in the data set?
Homework Answers
From the regression analysis, we know
Total sum of squares of Y = Sum of squares due to regression + Sum of squares due to error
Total sum of squares is the sum of square error if each observation is predicted as Y bar that is 6
Coefficient of determination = r square measure the proportion of variance explained by our regression equation
Here, r is 0.35 which means r square is 0.1225. Hence, 12.25 % of error is reduced if we use regression equation.
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