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Lecture 5

# Lecture 5 - regression line to make predictions for values...

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Least-Squares Regression The goal of least squares regression is to find an equation that best describes the relation between 2 variables that have a linear relationship as indicated by a scatterplot or linear correlation coefficient. The difference between the observed value of y and the predicted value of y (denoted ˆ y ) from the regression equation is the error or residual . residual = observed – predicted residual = y - ˆ y The line that “best” describes the relation between 2 variables is the one

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that makes the residuals as small as possible. Has the least error.
Equation of the Least-Squares Regression Line The equation is given by ˆ y = bx+a Where b is the called the slope and a is called the intercept b = SSxy SSxx a = y - b x

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Note: Never use the least-squares

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Unformatted text preview: regression line to make predictions for values of the predictor variable that are much larger or much smaller than those observed. If you do so, you are making predictions outside the scope of the model. Don’t use values extremely different than those used to find the line. Example: We type of linear relationship do you think this data has? Negative correlation X 2 3 5 6 6 y 6 5 5 3 2 2 x y 6 5 4 3 2 1 6 5 4 3 2 Scatterplot of y vs x Find the least-squares regression line. X Y X 2 Y 2 XY 6 36 2 5 4 25 10 3 5 9 25 15 5 3 25 9 15 6 2 36 4 12 6 2 36 4 12 ∑ x ∑ y ∑ x 2 ∑ y 2 ∑ xy Scatterplot w/ regression line. x y 6 5 4 3 2 1 7 6 5 4 3 2 Scatterplot of y vs x...
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Lecture 5 - regression line to make predictions for values...

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