Linear Regression is one of the most important tools in a Data Scientist's toolbox. Here's everything you need to know in 3 minutes.
1. OLS regression aims to find the best-fitting linear equation that describes the relationship between the dependent variable (often denoted as Y) and independent variables (denoted as X1, X2, ..., Xn).
2. OLS does this by minimizing the sum of the squares of the differences between the observed dependent variable values and those predicted by the linear model. These differences are called "residuals."
3. "Best fit" in the context of OLS means that the sum of the squares of the residuals is as small as possible. Mathematically, it's about finding the values of ฮฒ0, ฮฒ1, ..., ฮฒn that minimize this sum.
4. Slopes (ฮฒ1, ฮฒ2, ..., ฮฒn): These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant.
5. R-squared (Rยฒ): This statistic measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data.
6. t-Statistics and p-Values: For each coefficient, the t-statistic and its associated p-value test the null hypothesis that the coefficient is equal to zero (no effect). A small p-value (< 0.05) suggests that you can reject the null hypothesis.
7. Confidence Intervals: These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level).