A simple linear regression, y = β0 + β1X + e, is estimated with cross-sectional data. The resulting residuals e, along with the values of the explanatory variable x, are shown below.
x 1 2 5 7 10 14 15 20 24 30
e -2 1 -3 2 4 -5 -6 8 11 -10
(a) Graph the residuals e against the values of the explanatory variable x and look for any discernible pattern. (b) Which assumption(s) is being violated? Discuss its consequences and suggest a possible remedy. (c) List the three OTHER common violations associated with OLS. Discuss why they might occur, list their consequences, and suggest ways in which they can be corrected.