A student working on a summer internship in the economic research office of a large corporation studied the relation between sales of a product (Y, in million dollars) and population (X, in million persons) in the firm's 50 marketing districts. the normal error regression model was employed (Y= b0 + b1*Xi + e). The student first wished to test whether or not linear association between Y and X existed. The student accessed a simple linear regression program and obtained the following information on the regression coefficients:
Parameter Estimated Value 95% Confidence Interval
Intercept...................7.43119...............-1.18518 ; 16.0476
Slope......................0.755048...............0.452886 ; 1.05721
(a) The student concluded from these results that there is a linear association between Y and X. Is the conclusion warranted? What is the implied level of significance?
(b) Someone questioned the negative lower confidence limit for the intercept, pointing out that dollar sales cannot be negative even if the population in a district is Zero. Discuss.