In the situation of given problem, test for the existence of a linear relationship between the two variables.
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.