Linear Regression is one of the most important tools in a Data Scientist's toolbox.
Yet it's super confusing for beginners.
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Yet it's super confusing for beginners.
Let's fix that: π§΅
1. Ordinary Least Squares (OLS) Regression
Most common form of Linear Regression. 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).
Most common form of Linear Regression. 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. Minimize the Sum of Squares
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."
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
"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 Ξ²0, Ξ²1, ..., Ξ²n that minimize this sum.
"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 Ξ²0, Ξ²1, ..., Ξ²n that minimize this sum.
4. Coefficients (Ξ²1, Ξ²2, ..., Ξ²n):
These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant.
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 (RΒ²):
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.
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.
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).
These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level).
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That's a wrap! Over the next 24 days, I'm sharing the 24 concepts that helped me become an AI data scientist.
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