Nvidia Interview Question | R²
Question
You have built a multiple regression model. Your model R² isn’t as good as you wanted. For improvement, you remove the intercept term, your model R² becomes 0.8 from 0.3. Is it possible? How?
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Answer ( 1 )
Yes, it is possible. We need to understand the significance of the intercept term in a regression model. The intercept term shows model prediction without any independent variable i.e. mean prediction. The formula of R² = 1 – ∑(y – y´)²/∑(y – ymean)² where y´ is the predicted value.
When the intercept term is present, R² value evaluates your model wrt. to the mean model. In absence of the intercept term (ymean), the model can make no such evaluation, with the large denominator, ∑(y – y´)²/∑(y)² equation’s value becomes smaller than actual, resulting in higher R².