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Lecture

# CH 15 textbook notes

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University of Toronto St. George

Sociology

SOC202H1

Scott Schieman

Winter

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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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