For the situation of given problem, find the standard errors of the estimates of the regression parameters; give an estimate of the variance of the regression errors. Also give a 95% confidence interval for the true regression slope. Is zero a plausible value for the true regression slope at the 95% level of confidence?

Problem
Recently, research efforts have focused on the problem of predicting a manufacturer's market share by using information on the quality of its product. Suppose that the following data are available on market share, in percentage (Y ), and product quality, on a scale of 0 to 100, determined by an objective evaluation procedure (X ):

X: 27 39 73 66 33 43 47 55 60 68 70 75 82

Y: 2   3   10  9  4   6   5   8   7   9 10 13 12

Estimate the simple linear regression relationship between market share and product quality rating.