Code in R.

library (multcomp) 1. Model read in terms of female, schtyp and ses (as a factor); o = lm(read female + schtyp + factor(ses)). 2. Show the first few rows of the design matrix. 3. Calculate (XT X)-ly where Y is the reading score and X is the design matrix. 4. Compare the value computed in the previous step to the coefficients from the lm. Are they the same? 5. Use the "waldtest function of the library lmtest to test the null hypothesis that the factor ses explains no variation in reading scores. 6. Repeate the last step manually using syntax like t(coef(o)[4:5]) %*% solve(vcov(o))[4:5] %*% coef(o)[4:5] to create the test statistic and using an F-test