A study was conducted attempting to relate home ownership to family income. Twenty households were selected and family income was estimated, along with information concerning home ownership ( \(y=1\) indicates yes and \(y=0\) indicates no). The data are shown below.

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 income. Is there any evidence that this quadratic term is required in the model?

Transcribed Image Text:

Home Ownership Home Ownership Status Household Income Status Household Income 123456rxad 38,000 0 11 38,700 1 51,200 1 12 40,100 0 39,600 0 13 49,500 1 43,400 1 14 38,000 47,700 0 15 42,000 1 53,000 0 16 54,000 1 7 41,500 17 51,700 8 40,800 9 45,400 10 52,400 1111 0 18 39,400 19 40,900 20 52,800 1