Problem 4 Suppose we want to understand the impact of a categorical variable X with 6 levels on an outcome variable Y. Our sample size is n = 20. We run a linear regrssion model including also 7 other continuous variables. For the full model SSEFHH = 21.5 and 2 (a) How many coefcients will the regression model include if we code the categorical variable X using dummy variables? (b) Suppose we want to test if the categorical variable X is associated with the out come variable Y. We run a reduced linear regression model and we obtain that SSEreduced = 40. Compute the F ratio in this case. (c) The Fratio is distributed as a random variable F NU M, D E N. Compute the degrees of freedom N U M and DEN in this case. (d) Suppose that for a level of signicance oz, the corresponding theoretical quantile is F NUM, D EN,1_,1 = 2.1. Can we deduce that X has a significant effect over Y