Using the Least Squares Regression Line to Model a Relationship Between Variables (VCE SSCE General Mathematics): Flashcards

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Using the Least Squares Regression Line to Model a Relationship Between Variables
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Least squares regression line purpose

Best-fitting straight line through data for predictions

Form of regression equation

y=a+bxy = a + bx

Response variable in y=a+bxy = a + bx

yy (what we're trying to predict)

Explanatory variable in y=a+bxy = a + bx

xx (what we use to make predictions)

Slope bb interpretation in regression

Average change in yy per one-unit increase in xx

Intercept aa interpretation in regression

Average value of yy when x=0x = 0

Interpolation definition

Predicting within data range (reliable)

Extrapolation definition

Predicting outside data range (unreliable)

r2r^2 (coefficient of determination) meaning

Proportion of variation in yy explained by xx

Residual formula

Actual value - predicted value

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