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CH 15 textbook notes

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University of Toronto St. George
Scott Schieman

CH15 – BIVARIATE CORRELATIONSHIP AND REGRESSION: HYPOTHESIS TESTING  Hypothesis Test o t-statistic of the sample? o First compute ̅ and ̅ o Then compute SCP and TSS o Find Pearson’s r correlation coefficient, regression coefficient b  Larger slope and smaller standard error yield stronger evidence o Then use ̅and ̅ and b to compute a against the null hypothesis o Then specify regression line equation, plot it w/ lowest & highest X  Standard Error of the slope ( ) values on the scatterplot  Estimates the degree of sample-to-sample variation if  6 steps of statistical inference and 4 aspects of a relationship regression slopes were calculated from many random o Requirements: samples of size n  There is one representative sample from a single population  A small standard error implies a higher likelihood that  There are two interval/ratio variables most of the sample slopes would be near the true  There are no restrictions on sample size, but generally, the larger population slope the n the better  Larger standard error implies that the regression  Scatterplot of coordinates of the two variables fits a linear coefficient estimate may not accurately reflect the true pattern relationship between X and Y in the population o Existence of a Relationship  Does a linear relationship between X and Y truly exist in the population or is the linear pattern in this sample the result of √ ∑( ̅) sampling error?  ρ (rho) corresponding parameter of Pearson’s r statistic  Standard deviation of the residual ( )  measures the tightness of fit of coordinates around the ∑ regression line for the population √ √  if there’s no relationship in the population then ρ = 0  Pearson’s r will = 0 give or take sampling error
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