Q1

The dataset ex0923 in Sleuth3 contains a subset of the National Longitudinal Study of Youth survey with annual incomes in 2005, intelligence scores (AFQT) measured in 1981 and years of Education completed, for 1306 males and 278 females. Of interest is whether male incomes differ from female incomes, after accounting for education and intelligence.

library(Sleuth3)
?ex0923

1. Use plots to explore the relationship between income and intelligence, income and education, and intelligence and education. Comment on the relationships, the need for transformation, and possible outliers.

2. Obtain the least squares regression fit of the model: $\mu \\{\log(\textit{Income2005} )\, | \, \textit{AFQT, Educ, Gender} \\} = \beta_0 + \beta_1 \textit{male} + \beta_2\textit{AFQT} + \beta_3 \textit{Educ}$ where male is an indicator variable for the subject being male.

3. Write a statistical summary, interpreting the parameter \(\beta_1\), in the context of the study.

Q2

The dataset ex0722 in Sleuth3 contains measurements of crab claw size and force for three crab species.

1. Produce a scatterplot of log Force on log Height, with the three species distinguished by different colours or shapes.

2. Fit a separate lines model of log Force as a function of log Height for the three species.

3. Summarise the differences in effect of log Height on mean log Force between the three species. This question is asking specifically to compare the slopes, you may summarise your answer on the log scale (i.e. you do not need to backtransform), but you should compare all species to each other.