4. (a) Log-linear models are often used to model contingency tables. In terms of table and model counts for a two-way table, what is the significance of including (i) an intercept? (ii) an intercept and precisely one factor? (iii) an intercept and both main factors? (5 marks) (b) A market researcher is interested in the factors that might effect movie ratings and has found the following table that gives the number of films by category of ratings and film release year, 2000 2005 2010 2015 7.5 - 7.75 42 37 39 26 7.75 - 8 37 45 40 39 8- 8.25 15 11 16 11 8.25 - 8.5 8 6 7 8 Columns two through to four are the first year of the five year period during which the films were released. Rows two through to four are the category of film rating scores. The market research calculated two log-linear models (below) the first with both factors included and the second with just the ratings factor