Consider a binary response variable y and an explanatory var

Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.

Test for the significance of the intercept and the slope coefficients at a 5% level in both models

What is the predicted probability implied by the linear probability model for x = 20 and x = 30? (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places)

What is the predicted probability implied by the logit model for x = 20 and x = 30? (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places)

Solution

Now, for the variables to be significant at 5% level, the p-value of the must be less than 0.05

Thus,

For LPM, the constant term is significant but the coefficient of the x-term is not significant.

For the Logit model both the intercept and the x-term are significant

Since,

for the LPM the coefficient of the constant term is insignificant, we model will consist of only a constant term

y-hat = -0.72 (which is a constant straight line estimate) for both X=20 and X=30

For the logit model,

y-hat = -6.2 + 0.26(X)

X = 20 ----->

y-hat = -1

X = 30 ----->

y-hat = 1.6

We see that the probability values do not necessarily fall in the range 0 to 1 as they should actually since these are just the estimated values from the model.