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Inference for Regression Slope AP Statistics Chapter 27 a.k.a., “the end”

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2 goodness- of-fit test ??? 2 test of homogeneity 2 test of independence 1 row or column (1 sample) 2-way table (2+ samples) 2-way table (1 sample)

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2 goodness- of-fit test t-test and t-interval for regression slope 2 test of homogeneity 2 test of independence 1 row or column (1 sample) 2-way table (2+ samples) 2-way table (1 sample)

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What would a scatterplot look like if there is NO ASSOCIATION??? If there is no association, we say that the slope is “zero”

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An Example: Body Fat and Waist Size

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Assumptions/Conditions for regression inference Does the data appear to be linear?Does the data appear to be linear? Do we have a random sample? This helps to check the independence assumptionDo we have a random sample? This helps to check the independence assumption Does the plot thicken? The plot should NOT thicken.Does the plot thicken? The plot should NOT thicken. Nearly Normal Condition Histogram of residuals should be unimodal and roughly symmetric, without outliersNearly Normal Condition Histogram of residuals should be unimodal and roughly symmetric, without outliers Degrees of freedom: df = n – 2

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If all assumptions are true, the IDEALIZED regression model would look like this: We can depict our distribution like this:

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Regression Inference Define 1 (“true mean change in y for each unit increase in x”) t-test for regression slopet-test for regression slope H o : 1 = 0 H a : 1 ≠ 0 and continue as we would with any other t-test. obs – exp st. dev Confidence interval for 1 (regression slope)Confidence interval for 1 (regression slope) statistic ±crit. value × st. err

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(examples on computer printout worksheet) 27 Worksheet - Computer Printout Regression T-Test Practice

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Homework #27 Group Quiz next time (Ch. 26 – 27)

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