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Inference for Linear Regression (C27 BVD)

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* If we believe two variables may have a linear relationship, we may find a linear regression line to model that relationship. * But, if we do not have the entire populations for both variables, we may sample from the population and find a sample regression line using procedures we already learned. * Mainly we would look at the slope as a good indicator of a linear relationship – if there is no linear relationship the slope for the population regression line should be 0.

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* Linear – check the scatterplot for a straight relationship and residual plot for no patterns. * Independent – 10% condition (sample is no more than 10% of population) * Normal – Make a histogram or NPP of residuals to make sure there is no strong skew. * Equal Variance – The amount of scatter of residuals should be roughly the same (no fanning). * Random sampling/assignment

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* The sampling distribution for slope is unimodal and symmetric and if conditions are met a t- distribution is an appropriate model. * The interval is b +/- t* s r /(s x sqrt(n-1)) * Where s r is std dev of residuals and df = n-2 and the whole denominator is SE. * Use LinRegTInt on calculator

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* Usually H 0 is that B 0 = 0 (remember: use Greek (Beta) for parameters for the population) * Can be one or two-tailed alternate. * Test statistic t =(b – B 0 )/SE * Can use t-table for df = n-2 * Use LinRegTtest on calculator * On calculator test where you choose alternate, you will see both Beta and Rho, the population correlation coefficient. Testing for zero slope works the same as testing for zero correlation so the calculator just does both.

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Inference for Linear Regression Conditions for Regression Inference: Suppose we have n observations on an explanatory variable x and a response variable.

Inference for Linear Regression Conditions for Regression Inference: Suppose we have n observations on an explanatory variable x and a response variable.

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