Regression Analysis: Lab 8 Introduction to Modelling with a Categorical (Dichotomous) Outcome Mahrita.Harahap@uts.edu.auMaths Study Centre CB04.03.331 Open 11am – 5pm Semester Weekdays Check out www.khanacademy.org This presentation can be found at:www.mahritaharahap.wordpress.com/teaching-areas/

Marking Scheme: 0 if less than 50% attempted, 1 for more than 50% attempted but less than 50% correct, 2 if more than 50% correct.

FEEDBACK FOR LAB 7 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)=σ2 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).

FEEDBACK FOR LAB 7

A) Testing for Association between two variables:Ho: No association between the two variables (in the population) so any pattern we see is just due to random variation. Ha: An association exists between the two variables (in the population).Test Stat:

X2 follows a chi-squared distribution with (rows-1)×(columns-1) degrees of freedom.If X2 < X2

(rows-1)×(columns-1) , this means p-value<α, so we do reject the null hypothesis. We have enough statistical evidence to prove an association exists between the two variablesIf X2 > X2

(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

LAB 8 - INTRODUCTION TO MODELLING WITH A CATEGORICAL (DICHOTOMOUS) OUTCOME

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)