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What heteroskedasticity is: Recall that one of the assumptions for applying Ordinary Least Squares is that the variance of the residuals is constant V(ε)=σ 2 Otherwise known as Homoscedastic. If the residuals do not have constant variance, they are said to be Heterocedastic. When residuals are heteroscedastic (non-constant variance), we can fix them either by: *Transforming y to stabilise the variance - If series that are growing exponentially often appear to have increasing variability as the series rises over time, view logarithmized data. *Apply a weighted least squares estimation method, in which OLS is applied to transformed or weighted values of X and Y. The weights vary over observations, usually depending on the changing error variances. *Use a different specification for the model (different X variables).

A) Testing for Association between two variables: H o : No association between the two variables (in the population) so any pattern we see is just due to random variation. H a : An association exists between the two variables (in the population). Test Stat: X 2 follows a chi-squared distribution with (rows-1)×(columns-1) degrees of freedom. If X 2 X 2 (rows-1)×(columns-1), this means p-value>α, so we do not reject the null hypothesis. We do not have enough statistical evidence to prove an association exists between the two variables

B), C), D) and E) You can carry over the Gender*GP visits Cross Tabulation table to Excel by right clicking the table and select “copy special”, select “excel worksheet” then pasting on Excel to find your Odds=p/(1-p), Odds Ratios and Relative Risk Ratios. D) Odds Ratios are defined as the ratio of success to failure: Odds Ratio (female vs male)=Odds(female)/Odds(male) The odds for a female visiting the GP 3 or more times are ….. times higher than the odds of a male visiting the GP 3 or more times. E)Relative Risk (female vs male)= The relative risk for females visiting the GP 3 or more times is …. times higher compared to males.

F) same as A) G) same as B) H) same as D)