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 odds in favour 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 odds in favour 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 odds in favor of a success for a given value of X in a logistic regression model can be calculated using the formula: $$ \text{Odds} = \exp(\text{Intercept} + \beta \times X) $$ where $\beta$ is the coefficient for the variable X. Plugging in the given values: $$ \text{Odds} = \exp(-4.00 + 0.10 \times 25) = \exp(-4.00 + 2.5) = \exp(-1.5) = 0.2231. $$

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