(10 points) (Adapted from: Dobson and Barnett) Suppose that the data presented below are from an investigation into satisfaction with housing conditions in Aarhus, Denmark. Suppose that residents in selected areas living in rented homes built between 1960 and 1968 were questioned about their satisfaction and the degree of contact with other residents. The data were tabulated by type of housing. Table 2: Satisfaction with housing conditions Satisfaction Low Medium High Contact with other residents Low High Low High Low High Tower block 65 19 54 41 100 110 Apartment 30 25 76 116 151 271 House A visualization of the data is presented below. Proportion 0.4 0.6 0.8 1.0 0.0 0.2 Low Tower Block High Contact H 0.2 Proportion 0.4 0.6 0.8 1.0 00 Low M H 101 121 90 145 62 172 Apartment High Contact H- Proportion 0.0 0.2 0.4 0.6 0.8 1.0 T T House Low High Contact M 0 (3 points) The researchers wish to understand what factors are associated with "Low" housing satisfaction, and what factors are associated with "High" housing satisfaction, each relative to "Medium" housing sat- isfaction. They decide to fit a nominal logistic regression model (specifically: the baseline category logit model) using "Medium" as the reference category. They use both Contact and Housing type, coded as cat- egorical variables, as main effects. Write down the model in this setting. If you want to use numerical coding, please use: - Satisfaction: 1-Low, 2-Medium, 3=High Contact: 1 Low, 2=High - Housing: 1=Tower Block, 2=Apartment, 3=House Be sure to define any additional notation you use.