If other factors are held constant and the Pearson correlation between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.

Question

If other factors are held constant and the Pearson correlation between X and Y is r = 0.80, then the regression equation will produce more accurate predictions than would be obtained if r = 0.60. True or false?

Answer 1

r is used to assess the strength of a linear relationship between X and Y. r can take on any value between -1 (perfect negative linear relationship) and +1 (perfect positive relationship). r² measures the amount of variation in the Ys account for by the Xs. Since r=0.8 > r=0.6, the strength of the linear relationship is stronger. Also when r=0.8, r²=0.64 (or 64%) of the variatioon in Y due to X compared to r=0.6 and r² =0.36 (or 36%) of variation in Y due to X. If X and Y are not spuriously associated variables, i.e. using brand T toothpaste causes an increased number of solar flares, then within the range of the data, predictions should be more accurate.

Answer 2

The closer the r value is to 1, the stronger the relationship. Also, it would make for a higher coefficient of determination (r²), so a higher percentage of data could be explained by the regression equation. So, yes, this is a true statement.