The following statistics were calculated from pairs of observations where X represents the independent variable and Y represents the dependent variable.
Sigma x = 511
Sigma x squared = 34,234.5
Sigma y = 314
Sgima y squared = 13,036
Sigma xy = 19,064
n = 8
a. Determine the least squares line.
b. Determine the sample correlation coefficient between X and Y.
c. Determine if there is a linear relationship between X and Y at the .10 significance.
d. Find a 90% confidence interval for the slope of the regression line.
e. Find a 90% confidence interval for the mean of Y if X = 60.
f. Find a 90% prediction interval for Y if X = 60.
g. What are the necessary assumptions for the validity of the procedure in parts c, d, e, and f.