4.14 The table below presents the test-firing results for 25 surface-to-air antiaircraft missiles at targets of varying speed. The result of each test is either a hit (y = 1) or a miss (y = 0). Test 1 2 3 4 5 6 7 8 9 10 11 12 13 Target Speed x (knots) 400 220 490 210 500 270 200 470 480 310 240 490 420 y 0 1 0 1 0 0 1 0 0 1 1 0 0 Test 14 15 16 17 18 19 20 21 22 23 24 25 Target Speed x (knots) 330 280 210 300 470 230 430 460 220 250 200 390 y 1 1 1 1 1 0 0 0 1 1 1 0

(a) Fit a logistic regression model to the response variable y. Use a simple linear regression model as the structure for the linear predictor.

(b) Does the model deviance indicate that the logistic regression model from part

(a) is adequate?

(c) Provide an interpretation of the parameter ßx in this model.

(d) Expand the linear predictor to include a quadratic term in target speed. Is there any evidence that this quadratic term is required in the model?