4.1. The following statistics were calculated from pairs of observations where X represents the independent variable and Y represents the dependent variable.Sigma x = 511Sigma x squared = 34,234.5Sigma y = 314Sgima y squared = 13,036Sigma xy = 19,064n = 8a. 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.
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