17.5. Predicted probabilities (worked example)#

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A logistic regression model describes whether the probability of voting for Candidate X in an election depends on $x$ = the voter’s total family income (in thousands of dollars) the previous year. The prediction equation is:

$\log{ \left[ \frac{p(y=1)}{1-p(y=1)} \right]} = -2.00 + 0.03x $

Before we get to python, this exercise is a chance to practice converting logistic regression output into predicted probabilities by hand (i.e., by calculator or in Excel!) to help you see what is going on.

  • Identify $\beta$ and interpret its sign

  • Find the estimated probability of voting for the candidate when income = 10,000.

  • At which income level is the estimated probability for the candidate equal to 0.50?