11-06 math

Therefore the strength of a regression coefficient

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Unformatted text preview: correlation. When a regression coefficient is negative, the predictor has a negative effect, just like with a negative correlation. The magnitude or absolute value of bi tells how strong the effect is. If bi is near zero, then Xi has a weak effect on the outcome, just like with a correlation near zero. If bi is large (either positive or negative), then Xi has a strong effect on the outcome, just like with a correlation near ±1. The difference between regression coefficients and correlations is that regression coefficients aren’t standardized, meaning they’re not restricted to lie between  ­1 and 1. Therefore, the strength of a regression coefficient needs to be interpreted in terms of the ˆ units of the predictor and outcome variables. In general, bi tells how many units Y increases by for every unit increase in Xi. For example, if Xi is height (in inches) and Y is how long it takes a person to run a mile (in seconds), bi = 7 would mean that for every extra inch of height, a person tends to take 7 seconds longer to run a mile. A negative coefficient means a decrease; e.g., bi =  ­5 would mean that for every extra inch of height, a person tends to take 5 seconds less to run a mile. The b0 variable is a special regression coefficient called the intercept. Just like the intercept ˆ of a simple line, b0 tells what the value of Y is when all the Xis are zero (i.e., where the line intersects the Y axis). If zero isn’t a sensible value of any of the predictors (e.g., no one is 0 inches tall), then the intercept taken by itself won’t be a very sensible value for the outcome (e.g., it could be  ­50 seconds). Therefore, we generally don’t think too hard about what the value of the intercept indicate...
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This document was uploaded on 02/25/2014 for the course PSYC 3101 at Colorado.

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