Run a regression analysis on the following bivariate set of data with y as the response variable.
x
y
33.4
41.9
38.6
75.5
20.9
-10.4
45
33
31.8
30.3
20.4
15
29.3
38.8
34.2
53.1
35.5
58.4
22
21.4
30.1
22.1
29.5
41.6
Find the correlation coefficient and report it accurately to three decimal places.
r =
What proportion of the variation in y can be explained by the variation in the values of x? Report the 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 +
Predict what value (on average) for the response variable will be obtained from a value of 24.5 as the explanatory variable. Use a significance level of α=0.05 to assess the strength of the linear correlation.
What is the predicted response value? (Report the answer accurately to one decimal place.)
y =