Question

# Run a regression analysis on the following bivariate set of data with y as the response...

Run a regression analysis on the following bivariate set of data with y as the response variable.

x y
48 41.8
39.2 67.4
34.7 68.4
42.9 50.2
49 50.6
45.6 57
58.7 29.7
40.5 68.4
47.4 34.7
45.7 50.9
38.9 47.7
40.9 53.6

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² = %

Based on the data, calculate the regression line (each value to three decimal places)

y =  x +

13.Predict what value (on average) for the response variable will be obtained from a value of 40.5 as the explanatory variable. Use a significance level of α=0.05α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)
y =

 SUMMARY OUTPUT Regression Statistics Multiple R 0.80159 R Square 0.642546 Adjusted R Square 0.606801 Standard Error 7.857172 Observations 12 ANOVA df SS MS F Significance F Regression 1 1109.729 1109.729 17.97564 0.001717 Residual 10 617.3515 61.73515 Total 11 1727.08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 122.7141 16.90241 7.260157 2.73E-05 85.05322 160.3751 85.05322 160.3751 x -1.60333 0.378164 -4.23977 0.001717 -2.44593 -0.76073 -2.44593 -0.76073