The table below presents the test - fi ring 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).

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 β1 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?

Test Target Speed, x (knots) y Test Target Speed, x (knots) y 123456 69 400 0 14 330 1 220 1 15 280 1 490 0 16 210 1 210 1 17 300 1 500 0 18 470 1 270 0 19 230 0 200 1 20 430 0 8 470 9 480 10 310 11 240 12 490 13 420 TTIIIO 0 21 460 0 0 22 220 1 1 23 250 1 1 24 200 1 0 25 390 0 0