simple regression noteshells

simple regression noteshells - Simple Regression 3:...

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1 Simple Regression 3 1 Simple Regression 3: Inference and Prediction Sections 13.7-13.8 Simple Regression 3 2 Our Examples h Site.XLS – Annual sales per store at Sunflowers Apparel predicted by the size of the store. h ________ – h A new one __________ –
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2 Simple Regression 3 3 The simple regression model h We fit a model of the form: h And then we checked it to determine if this was a reasonable way to view the data. h At this point we might be interested in using the model for statistical inference. X b b Y 1 0 ˆ + = Simple Regression 3 4 Statistical inference Some of the things we want to do: 1. Test to see if there is a significant relationship between X and Y 2. Make an interval estimate of the effect of X on Y 3. Predict the value of Y that may occur at a specific X
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3 Simple Regression 3 5 Testing for significance h Any time we have a set of data we can go ahead and get a correlation or regression. Excel will give us the numbers. h But, is something really there or is it “coincidence”? h We can test for significance. Simple Regression 3 6 A test on the correlation h Earlier we had a “quick rule” about the correlation. h It said correlation is significant if ______. h Here we look at a more formal test that can use a different α or can be configured with a one-sided hypothesis.
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4 Simple Regression 3 7 The T-test (page 500-501) h The hypotheses are: h The standard error for the correlation r is: h Calculate the T- stat. The formula is: 2 1 2 - - = n r s r 2 1 0 2 - - - = n r r t STAT 0 : 0 : 1 0 = ρ H H Simple Regression 3 8 Test for new example Data set _____________ X= ________ Y = _________ n = ___ r = ___
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5 Simple Regression 3 9 Inference about the slope ( β 1 ) h In a regression, b 1 is our estimator of the population slope. h It is a function of the sample data, so the estimator b 1 is a random variable that follows some distribution. h The standard deviation in this distribution is the standard error for the slope estimate 1 b s Simple Regression 3 10 Interval estimate of slope h A confidence interval estimate of the population’s true slope ( β 1 ) is given by: b 1 ± t · h t is a value from the T-distribution with n-2 degrees of freedom 1 b s
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6 Simple Regression 3 11 Output for Sunflowers sales regression interval s b b 1 1 Simple Regression 3 12 Computation of interval
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simple regression noteshells - Simple Regression 3:...

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