Discussion questions#
Linear regression can answer research questions typically reserved for specialty statistics like the t-test and ANOVA. For example, Pearson correlation coefficient has the form of \(r = \frac{COV[X,Y]}{STD[X]STD[Y]}\), how does this compare to the ordinary least squares solution for \(\hat{\beta}\)? Provide a quantitative comparison of the two methods. Note: The unstandardized beta (B) represents the change in Y for a one-unit change in X. The standardized beta (β) represents the change in Y in standard deviation units for a one standard deviation change in X.
Provide an explanation for why polynomial models still meet the assumptions of normal linear regression. Justify against each of the 4 assumptions for ordinary least squares regression.