The correlation coefficient is a measure of linear association. Suppose x takes on values evenly over the range from –10 to 10, and that E[y/x] = x 2 . In this case, the correlation of x and y is...

The correlation coefficient is a measure of linear association. Suppose x takes on values evenly over the range from –10 to 10, and that E[y/x] = x². In this case, the correlation of x and y is zero, even though there is clearly a systematic relationship. What does this suggest about the need to test model assumptions? Using a statistical package, generate a random sample of 100 values of x uniformly distributed on [–10, 10], compute E[y|x] for each value of x, add randomly generated standard normal errors to get the 100 values of y, and check the sample correlation of x and y.