Repeat problem 1 for the data of problem 3.

Problem 1
Carry out an F test for a linear relationship in problem 2. Compare your results with those of the t test.

Problem 2
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.

Problem 3
For the data given below, regress one variable on the other. Is there an implication of causality, or are both variables affected by a third?