Simple Linear Regression

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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. 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 Linear Regression

Variability Explained Variability Explained Visualizing r2 r2 = Variability Explained Total Variability in y Variability Explained Height Weight Total Variability in Y Vrbility Remain Linear Regression

r2 doesn’t depend on x because of homoscedasticity Variability Explained Height Weight Total Variability in Y Vrbility Remain 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 Linear Regression