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8 - Prediction Part 2

# 8 - Prediction Part 2 - Quick Recap We want to predict a...

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Quick Recap We want to predict a score on Y ( Y’ ) based on a score on X. We can use the equation for a straight line to make this prediction (assuming linear relationship) Y’ = bX + a Want to find the line that minimizes the distance between itself and all Y scores

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Finding the Regression Line What values must we use for our line in order to find the regression line? One option: Use the standard scores of Y and X z’ Y = r z X In this formula, r = slope of the line Remember that z scores are centered around the mean (z of 0 = raw score mean) Therefore, intercept of this formula = 0
For r = 0, z’ Y will always be zero Can generalize If r (or b) equals zero, Y’ will always be mean of Y • z’ y = rz x is conceptually useful, but difficult to predict with.

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We will use a raw score formula to find our regression line • z’ Y = r z X is Q Q Q Q Q Q Q Q - = - X Y S X X r S Y Y ' Solving for Y’ gives us the following:
Raw Score Regression Formula Y X S S r X S S r Y X Y X Y + - = 220d

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Y X S S r X S S r Y X Y X Y + - = 220d b a
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8 - Prediction Part 2 - Quick Recap We want to predict a...

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