Consider the setup of the previous problem (housing data with three covariates 2:1, 2:2 and $3), but assume that we look at a different subset of the data, now with sample size n = 100. Consider the the following ve models: (Note that the models are NOT named the same way as the previous problem.) #31: y=o+a zz: y=5o+1m1+2m2+65 M3: y=50+51$1+2$2+53m+a (2) 4: y=3o+51$1+52$2+53$3+ M5: y=50+51m1+52$2+53m1m2+a Either treat these model expressions as those of the population level (i.e., y, 3:1, mm, etc. are all scalars), or if you want to treat them as vector quantities, interpret the nonlinear operations elementwise, e.g. 221mg 6 R\" is a vector with ith element 3:412:42, where am is the 3th element of 2:1 E R\" and so on. (a) Specify which of the following pairs of models we can directly compare using an Ftest: (1 point each) 1 (Can Cannot) (M1, M2) 2. (Can Cannot) (Mgr/$3) 3. (Can Cannot) (Mgr/$4) 4 (Can Cannot) (M2, J5) ( 5. CanCannot) (M4,.5) (b) Can you compare the R2 of M2 to that of M3 without any computation? Justify your answer. (2 points) Suppose that each of the above models were fitted to the data and the following residual sum of squares (SSE) were obtained: Model .451 M2 .483 144 M5 SSE 3478.94 548.93 481.20 545.23 542.21 (c) What is the total sum of squares (SST) for this data? (2 points) Suppose that each of the above models were tted to the data and the following residual sum of squares (SSE) were obtained: Model M1 Jag M3 M4 M5 SSE 3478.94 548.93 481.20 545.23 542.21 (c) What is the total sum of squares (SST) for this data? (2 points) (d) Find the adjusted R2 for model M3. Is model M3 a good t? (4 points) (e) Test for the overall signicance of the regression relation in 2. Which model in (2) is the null model for this test? (4 points) (f) Perform an F-test for the signicance of 53 in model M3. (5 points) (g) Someone claims that the SSE is a good model selection criterion for choosing among M3, M4 and .435. Argue for or against. (3 points) (h) Overall, which model out of the ve given models should we pick? Justify your answer. (3 points) Scanned by CamScanner Scanned by CamScanner