Question

Examine classification using logistic regression. In R console, type mtcars. The dataset mtcars is a generic dataset in R. This dataset comprises of fuel consumption and 10 aspects of automobile design and performance for 32 automobiles. Using only the variables am (0 = automatic, 1 = manual) and mpg, your task is to fit a logistic regression model. Complete the following steps using R.

1. Create a scatter plot of am vs. mpg. Describe the relationship and explain why a simple linear regression model may not be suitable.
2. Using the variables am and mpg, fit a logistic regression model. Use the function glm().
3. Write the estimated logistic regression model from part #2 results.
4. Suppose a car has 16 mpg. How would you classify the transmission: automatic or manual? Explain and show how you classified the transmission.

Answer 1

We first load and perform the task with the following codeFrom the above graph we see that the data is not continuous and is distributed on the extremities of both the axis. Such problems cannot be accurately resolved or worked with a traditional linear regression approach as linear regression best deals with continuous forms of data. However we can solve this using a logistic regression approach which allows us to categorize variables based on their tags and are very useful when we need to categorize them as in this case of manual vs automatic

The logistic regression model can be viewed in the above segment of code with it's complete summary.

When tested with a value of mpg=16,we obtain that the probability that it has a manual transmission is very low and the cut off being as a value of 0.5 predicts that it is automatic in nature.

Note:This might not be the optimal combination of attributes which lead to an accurate prediction of the value seen and better predictions can be obtained through more efficient decisions of better correlated attributes