Statistician Frank J. Anscombe created a data set to illustrate the importance of doing more than just examining the standard regression output. These data are provided in the file P10_64.xlsx.
a. Regress Y1 on X. How well does the estimated equation fit the data? Is there evidence of a linear relationship between Y1 and X at the 5% significance level?
b. Regress Y2 on X. How well does the estimated equation fit the data? Is there evidence of a linear relationship between Y2 and X at the 5% significance level?
c. Regress Y3 on X. How well does the estimated equation fit the data? Is there evidence of a linear relationship between Y3 and X at the 5% significance level?
d. Regress Y4 on X4. How well does the estimated equation fit the data? Is there evidence of a linear relationship between Y4 and X4 at the 5% significance level?
e. Compare these four simple linear regression equations (1) in terms of goodness of fit and (2) in terms of overall statistical significance.
f. How do you explain these findings, considering that each of the regression equations is based on a different set of variables?
g. What role, if any, do outliers have on each of these estimated regression equations?