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 \((y=0)\).

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 \(\beta_{1}\) 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?

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Test Target Speed, x (knots) y Test Target Speed, x (knots) 1 400 0 14 330 1 234567890122 220 1 15 280 1 490 16 210 210 1 17 300 500 0 18 470 270 0 200 1 470 480 0 310 1 11 240 1 490 42222222 19 230 20 430 21 460 220 23 250 200 25 390 OT1I1O 420