Data science simplified: Entering the world of multivariate regression models

In the last article of this series, we discussed the story of Fernando, a data scientist who wanted to buy a car. He used a simple linear regression model to estimate car prices.

Fernando’s regression model predicted price based on the engine size, predicting one dependent variable using one independent variable.

This was the formula for his simple linear regression model:

price = β0 + β1 x engine size

The statistical package computed the parameters. The linear equation is estimated as:

price = -6870.1 + 156.9 x engine size

The model was also evaluated on two fronts:

• Robustness using hypothesis testing
• Accuracy using the coefficient of determination (aka R-squared)

Recall that R-squared explains the fraction of the variance between the values predicted by the model and the value as opposed to the mean of the actual. This value is between 0 and 1. The higher it is, the better the model can explain the variance. The R-squared for the model created by Fernando was 0.7503 (i.e. 75.03 percent on the training set). It means that the model can explain more than 75 percent of the variation.

However, Fernando wants to make it better. If he could feed the model with more inputs, would it improve its accuracy?

He decides to enhance the model by feeding it with more input data (i.e. more independent variables). He has now entered into the world of multivariate regression models.

The concept

Model formulation

Model building

Model interpretation

Model evaluation

Conclusion

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