We see that most used Corollas are around $10K and there are some at the tail end that over $25K. These might be newer cars with a lot of options. And there are fewer of them anyhow.

2. Data Transformation:

One of the main steps in the predictive analytics is data transformation. Data is never in the way you want them. One might have to do some kinds of transformations to get it to the way we need them to be either because the data is dirty, not of the type we want, out of bounds, and a host of other reasons.

In this case, we need to convert the categorical variables to numeric variables to feed into our linear regression model, because linear regression models only take numeric variables.

The categorical variable we want to do the transformation on is Fuel Types. We that there are 3 Fuel Types: 1) CNG 2) Diesel 3) Petrol

So, we can convert the categorical variable Fuel Type to two numeric variables: FuelType1 and FuelType2. We assign CNG to a new variable FuelType1 in which a 1 represents it’s a CNG vehicle and 0 it’s not. Likewise, we assign Diesel to a new variable FuelType2 in which a 1 represents it’s a Diesel vehicle and 0 it’s not.

So, what do we do with PETROL vehicles? This is represented by the case when BOTH FuelType1 and FuelType2 are zero.

3. Exploratory Data Analysis (EDA):

The next step in predictive analytics is to explore our underlying. Let’s do a few plots of our explantory variables to see how they look against Price.

4. Model Building: Linear Regression

Now that we have explored our variables, let’s a simple linear regression of Price against all the data we’ve collected.

We see from the output that our model prices 86.9%(see Multiple R square) of the variation in price using the explantory variables above. This is pretty decent.

However, we notice is that some coefficents are more statistically significant that others. For example, we find that Age is the most significant witha t-value of -46.889, followed by Weight with a t-value of 16.629. The least significant variables are Metallic Color and Number of Doors. This was also confirmed in our EDA graphs above.

Now, it’s generally NOT a good idea to use your ENTIRE data sample to fit the model. What we want to do is to train the model on a sample of the data. Then we’ll see how it perform outside of our training sample. This breaking up of our data set to training and test set is to evaluate the performance of our models with unseen data. Using the entire data set to build a model then using the entire data set to evaluate how good a model does is a bit of cheating or careless analytics.

5. Results with Training Data:

Here is the results using the first 1000 rows of data as training sample.

Interesting enough, the R-squared only changed nominally to 85.7% and the variables t-value also moved slightly onky. The statistically significant relationships remained the same. Good.

6. Model Evaluation: Linear Regression

The real test of a good model is to test the model with data that it has not fitted. Here’s where the rubber meets the road. We apply our model to unseen data to see how it performs.

7. Prediction using out-of-sample data.

Here are some common metrics to see how well the model predicts using various error metrics. The main takeway is we want our forecast errors to be as small as possible. The smaller the forecast error the better the model is at predicting unseen data.

ME is the mean error. The ideal ME is zero, which means on average the predicted value perfectly matches the actual value. This is rarely if ever the case. As in all things, we must determine what is an acceptable level of errors for our predictive analytics model and accept it. No such thing as a perfect model.

RMSE is root mean squared error. A mean squared error(MSE) is the average of the squared differences between the predicted value and the actual value. The reason we square is to not account for sign differences(negative differences and positive differences are the same thing when squared). RMSE brings it back to our normal unit by taking the square root of MSE>

MAPE stands for mean absolute percent error and express the forecast errors in percentages.

On average, our model had a forecast error of only 9.2%. Not bad for a first pass at this data set.

8. Conclusion

Hope you enjoyed this and are excited in applying predictive analytics models to your problem space.

In follow on blogs I’ll use the same data set but apply it with other predictive analytics methods and models to see how it performs.