Linear Regression Essentials
Understand how simple linear regression helps explain and predict variability in one variable based on another, visualizing coefficient of determination (r2), and assessing the strength of the relationship for better predictions in data analysis.
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Presentation Transcript
Simple Linear Regression Using one variable to 1) explain the variability of another variable 2) predict the value of another variable Both accomplished with the line that best fits a scatterplot. Slide #1 Linear Regression
Coefficient of Determination Proportion of the total variability in the response variable explained away by knowing the value of the explanatory variable Abbreviated with r2 Slide #2 Linear Regression
Visualizing r2 Variability Explained Total Variability in y r2 = Variability Explained Total Variability Remain Vrbility Weight in Y Height Slide #3 Linear Regression
r2doesnt depend on x because of homoscedasticity Variability Explained Total Variability Remain Vrbility Weight in Y Height Slide #4 Linear Regression
Coefficient of Determination Proportion of the total variability in the response variable explained away by knowing the value of the explanatory variable Abbreviated with r2 0 < r2 < 1 Closer to 1 is a stronger relationship Closer to 1 gives better predictions Slide #5 Linear Regression
