Problem Sheet 4 -- ANOVA and Linear Regression

ANOVA

Consider the inbuilt R dataset chickwts (you can access this in R using the data command data(chickwts)) which is comprised of experimental data on chicken weight for various types of feed.

Conduct an ANOVA analysis to determine if group affiliation has any influence on variance. Use an F-test to determine the significance of your finding.
Conduct post-hoc analysis for pairwise comparisons of means. For which food types are the mean chicken weights significantly different for an alpha level of 0.05?

F distributions

Devise a method that would allow you to determine F_{2,30} by direct sampling from normal distributions and implement it.

Linear regression

The lecture states that in linear regression the regression line always goes through the means of the independent/dependent variable. To explore this,

generate a dataset of 100 datapoints given by sampling two variables X and Z from a normal distribution with mean 100 and standard deviation 10 and calculating adding the sample points to obtain Y. What intercept and slope do you expect from linear regression? Calculate a line of best fit and check if it goes through the means of X and Y.

Prove the above statement analytically.