Refer to Exercise 11.53.
(a) Obtain the decomposition of the total y variability into two parts: one explained by linear relation and one not explained.
(b) What proportion of the y variability is explained by the straight line regression?
(c) Calculate the sample correlation coefficient between x and y.
Exercise 11.53
An experiment is conducted to determine how the strength y of plastic fiber depends on the size x of the droplets of a mixing polymer in suspension. Data of (x, y) values, obtained from 15 runs of the experiment, have yielded the following summary statistics.

(a) Obtain the equation of the least squares regression line.
(b) Test the null hypothesis H0 : β1 = -2 against the alternative H1: β1 (c) Estimate the expected fiber strength for droplet size x = 10 and set a 95% confidence interval.

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8.3 54.8