Simple Linear Regression

Statistics · Axiom Academy

LESSON Simple Linear Regression Understanding the relationship between two quantitative variables through the best-fit line The simple linear regression equation expresses the predicted value of the response variable as a linear function of the explanatory variable: y-hat (ŷ) = predicted value of the response variable b₀ = y-intercept (value of ŷ when x = 0) b₁ = slope (change in ŷ for each unit increase in x) x = value of the explanatory variable 2. Explanatory Variable vs Response Variable Understanding the roles of variables in regression is crucial for proper interpretation: The independent variable used to predict or explain changes in the response variable. Also called the predictor or independent variable. The dependent variable being predicted or explained. Its values respond to changes in the explanatory variable. 3. The Regression Line as "Best Fit" The regression line is positioned to minimize the sum of squared residuals (the vertical distances between data points and the line). This is called the least squares method . The "best fit" line is the one that minimizes the sum of all squared residuals. This ensures that the line is as close as possible to all data points collectively. 4. Making Predictions with the Regression Equation Once we have the regression equation, we can substitute any value of x to predict the corresponding value of y. To predict the test score for a student who studied 5 hours:

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