A study was recently done in which the following regression

A study was recently done in which the following regression output was generated using Excel.

Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

Regression Statistics 0.754525991i 0.569309472 Multiple R R Square Adjusted R Square Standard Error Observations 0.507782252 1.977472261 ANOVA df Significance F 36.18277975 36.18278 9.252969 0.018797 Regression 1 Residual Total 27.3727758 3.910397 8 63.55555556 P-value Lower 95% U r 9500 Intercept 4.822953737 2.20457789 2.187699 0.064899 -0.39004 10.03595 0.053825623 0.017694916 3.041869 0.018797 0.011984 0.095667 Coefficients Standard Error t Stat

Solution

Sol)

From above analysis The regression equation is

y=4.822 + 0.0538(X)

And the correlation coefficient is 0.7545

and Coefficient of determination is (R square ) is 0.5693

ie.,approximately 57 percent of the variation in the y variable is explained by the x variable