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
51.3 17.4
60.8 88.6
37.4 32.9
44.6 53.4
53.7 53.6
52.2 41.5
32.7 28.6
62.4 84.7
47.4 35.7
39.8 33.7
62.1 123
62 83.7

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)

ˆy=______+_______ x

Predict what value (on average) for the response variable will be obtained from a value of 47.4 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.)
ˆy=_______