regression II

regression II - Quantitative Methods Regression II March 4,...

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© John M. Ackroff 2008 Quantitative Methods Regression II March 4, 2008
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© John M. Ackroff 2008 Prediction The farther I am from X, the farther I’ll be from Y. The sign of ρ or r tells the direction The strength tells how far.
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© John M. Ackroff 2008 Predicting Y from X t y ‘ = r * t x ρ y ‘ = ρ * Z x When plotted on Z or t axes, The “best fit” line passes through the origin The slope of the “best fit” line = r or ρ. When we plotted lines against raw scores, the slope showed the sign of r or ρ, but did not indicate strength of the relationship. On X or t axes, we can see the strength Because we compute r or ρ from t or X scores.
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© John M. Ackroff 2008 Predicting Y from X Suppose I sample students from this class, and record their height, weight, and age. Suppose r HeightWeight = 0.95 If a person is 6’ tall, how much does he weigh?
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© John M. Ackroff 2008 Predicting Y from X If H = 5’9” and s H = 2” t 6’ = (6’ = 5’9”) / 2” = 3” / 2” = 1.5 ty’ = 1.5 * .95 = 1.42 If W = 150 and s W = 15 Y’ = 150 + 1.42 * 15 = 150 + 21.3 = 171.3
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© John M. Ackroff 2008 Summary We use X, X, and s X to compute t X . t Y ’ = r * t X We use t Y ’, s Y , and Y to compute Y’.
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© John M. Ackroff 2008 Remember We can predict Y from X When there is a reasonably strong relationship between X and Y We’ll get to what that means… When X is within the range of X scores of the sample we used to compute r .
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© John M. Ackroff 2008 Problem with using an estimate Suppose X and Y are unrelated. You draw a sample from the population. What’s the probability that r = 0? Really, really small. How far does r have to be from 0 before we can conclude that X and Y are actually related?
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© John M. Ackroff 2008 The Null Hypothesis (H 0 ) There is no difference. X and Y are not related. r = 0 We’ve seen this before.
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© John M. Ackroff 2008 Can we use our estimate? We have to look at the r table. If | r | > the critical value in the table, the value of r we computed from our sample is sufficiently unlikely to occur by chance that we conclude that it is real. There actually is a relationship between X and Y We can predict the value of one variable from the other.
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The Null Hypothesis I suspect that people who enjoy strongly flavored foods enjoy other extreme sensations. I’ll use scary movies as my other
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regression II - Quantitative Methods Regression II March 4,...

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