Suppose we are interested in predicting the current market value of houses in a particular city. We have collected data that comprises a random sample of 30 current house values (1,0006) together with their corresponding living area (100 z) and the distance in miles from the city center. Can Summarlls Cilycanta Value [10005 Am 1005 disarm miles 1 210.4 12.0 1.2 2 262.5 15.6 1.5 3 258.9 14.6 1.6 4 245.0 14.7 2.5 5 239.3 15.0 2.7 6 263.1 16.6 2.6 7 2032 12.0 3.2 8 2215 13.4 3.2 9 2072 14.0 4.1 10 2345 15.6 4.2 11 195.6 13.0 4.4 12 2223 145 4.7 13 1922 123 5.1 14 2466 17.7 5.3 15 216.5 15.3 5.5 16 224.0 13.0 1.3 1? 2415 145 1.6 16 245.5 14.3 1.9 19 263.4 15.8 2.4 20 264.4 16.6 2.6 21 269.9 172 4.0 22 2363 15.7 3.2 23 235.2 16.0 4.2 24 216.6 12.5 3.9 25 241;: 15.7 3.6 26 2375 15.6 4.5 27 130.8 12.6 4.6 23 200.5 13.4 5.0 29 205.0 13.7 5.1 30 2366 17.6 6.3 1. Let's build a multiple regression model that can successfully predict house values using the living area and distance variables. (a) What are the independent and dependent variables? (b) Write down the model. Don't forget to check your assumptions. (0) Interpret the coefcients. What do they mean in terms of our example? 2. Perform a hypothesis test for testing the overall model and each of the coefficients. What are the null and alternative hypotheses for each? Report the results of each test in APA format. 3. For a house that is 5 miles from the city center and is 1,400 ft, what is the expected house value