Consider a logistic regression model for the probability of a "success",given a quantitative variable X. $$\begin{array} { | l | c | }
\hline \text { Term } & \text { Estimate } \
\hline \text { Intercept } & - 4.00 \
\hline \mathrm { X } & 0.10 \
\hline
\end{array}$$ Use the output above to estimate the probability of a success when X = 25.
A)0.1824
B)0.8176
C)0.2019
D)0.7981
E)0.2231

Question

Consider a logistic regression model for the probability of a "success",given a quantitative variable X. $$\begin{array} { | l | c | } 
\hline \text { Term } & \text { Estimate } \
\hline \text { Intercept } & - 4.00 \
\hline \mathrm { X } & 0.10 \
\hline
\end{array}$$ Use the output above to estimate the probability of a success when X = 25.
A)0.1824
B)0.8176
C)0.2019
D)0.7981
E)0.2231

Quizplus · Accepted Answer

The logistic regression model is given by $ P(success) = \frac{1}{1 + e^{-(\beta_0 + \beta_1 X)}} $. Substituting the values, $ \beta_0 = -4.00 $ and $ \beta_1 = 0.10 $, and $ X = 25 $, we get $ P(success) = \frac{1}{1 + e^{-(-4 + 0.10 \times 25)}} = \frac{1}{1 + e^{-(-1.5)}} \approx 0.1824 $.

Consider a Logistic Regression Model for the Probability of a "Success",given