# Estimated Logistic Regression Equation

Using the generalized linear model, an estimated logistic regression equation
can be formulated as below. The coefficients a and b_{k} (k = 1, 2, ..., p) are determined
according to a maximum likelihood approach, and it allows us to estimate the
probability of the dependent variable y taking on the value 1 for given values of x_{k} (k
= 1, 2, ..., p).

#### Problem

By use of the logistic regression equation of vehicle transmission in the data set mtcars, estimate the probability of a vehicle being fitted with a manual transmission if it has a 120hp engine and weights 2800 lbs.

#### Solution

We apply the function glm to a formula that describes the transmission type (am) by the horsepower (hp) and weight (wt). This creates a generalized linear model (GLM) in the binomial family.

We then wrap the test parameters inside a data frame newdata.

Now we apply the function predict to the generalized linear model am.glm along with newdata. We will have to select response prediction type in order to obtain the predicted probability.

#### Answer

For an automobile with 120hp engine and 2800 lbs weight, the probability of it being fitted with a manual transmission is about 64%.

#### Note

Further detail of the function predict for generalized linear model can be found in the R documentation.