11-06 math

# E according to the null hypothesis that its true

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Unformatted text preview: on coefficients. Therefore, each bi has a sampling distribution, which represents the probabilities of all possible values we could get for bi if we replicated the experiment. Each bi also has a standard error, which as usual is the standard deviation of the sampling distribution. The standard error tells us how reliable our estimate is, meaning how far we can expect it to be from the true population value. We won’t go into detail about how the standard errors of the regression coefficients are calculated, because it’s much easier to use a computer for this. However, it’s important to understand what the standard errors can tell us. First, the standard error can be used to create a confidence interval for each bi, in the same way we create confidence intervals for means. I won’t describe the math, but the idea is the same as before: The confidence interval is centered on the actual value of bi obtained from the sample, and the width of the confidence interval is determined by the size of the standard error. The second thing we can use standard errors for is hypothesis testing. In regression, the most common hypotheses to test regard whether the predictors have reliable influences on the population. This corresponds to asking whether the true values of the regression coefficients are different from zero. For each predictor, Xi, the null hypothesis bi = 0 states that Xi has no reliable effect on Y (the alternative hypothesis is bi ≠ 0). Notice that there’s a separate null hypothesis for each predictor, and we can test each one individually. To test whether bi = 0, we calculate a t statistic equal to bi (the actual regression coefficient we obtained from our sample) divided by its standard error....
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## This document was uploaded on 02/25/2014 for the course PSYC 3101 at Colorado.

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