The compressive strength of an alloy fastener used in aircraft construction is being studied. Ten loads were selected over the range \(2500-4300\) psi and a number of fasteners were tested at those loads. The numbers of fasteners failing at each load were recorded. The complete test data are shown below.

a. Fit a logistic regression model to the data. 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. Expand the linear predictor to include a quadratic term. Is there any evidence that this quadratic term is required in the model?
d. For the quadratic model in part \(\mathrm{c}\), find Wald statistics for each individual model parameter.
e. Find approximate \(95 \%\) confidence intervals on the model parameters for the quadratic model from part \(\mathrm{c}\).

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Load, x (psi) Sample Size, n Number Failing, r 2500 2700 50 10 70 17 2900 100 30 3100 3300 60 21 40 18 3500 85 43 3700 90 54 3900 50 33 4100 80 60 4300 65 51