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CH 14 textbook notes

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Scott Schieman

CH14 – BIVARIATE CORRELATIONSHIP AND REGRESSION  CORRELATION – a systematic change in the scores of two interval/ratio  Understanding the Pearson’s r Formulation variables o Divide scatter plot into 4 quadrants and , note the relationship o 2 interval/ratio variables correlated (co-relate) when measurements  Quadrant 1 & 4 populated = negative relationship; Quadrant 2 & of one variable change in tandem with the other consistently from 3 populated = positive relationship; no pattern = no relationship case to case o All elements of r equation involve deviation scores o Usually: dependent variable (Y) and independent variable (X) o r gauges how deviation scores of Y and Y fluctuate together (covary) o Simple Linear Correlation and Regression – use formula for a straight  if positive relationship then expect samples on positive side of line to improve best estimates of a interval/ratio dependent variable also on the positive side of (Y) for all values of an interval/ratio independent variable (X)  denominator gauges how much total error X and Y have relative o Formula for straight line: to one another  Applies for interval and ratio measurements  assuming no relationship between X and Y  Used only when there’s a linear relationship between X and Y  numerator gauges how well X and Y fluctuate in a pattern  Graphical representation of the relationship between two interval/ratio  measures correlation effect of the relationship variables  perfect relationship: numerator will equal denominator o Scatterplot:  A two-dimensional grid of coordinates of two interval/ratio Regression Statistics variables, X and Y on the X-axis and Y-axis  Linear equation formula: o Coordinate:  A point on a scatterplot where the values of X and Y are plotted o First calculate the values of a and b then plug in X and solve for Y for a case o : the predict Y o Linear pattern:  An estimate of the dependent variable Y computer for a given  One where the coordinates of the scatterplot fall into a cigar- value of the independent variable X shaped pattern that approximates the shape of a straight line o : the Regression Coefficient or Slope  Identifying linear patterns  Effect on Y per 1-unit change in X o On scatterplot: coordinates in elongated cigar-shaped pattern  o : The Y-intercept or the constant linear relationship  Anchors the regression line to the Y-axis o POSITIVE CORRELATION – an increase in X is related to an increase in  Usually hypothetical point b/c there may be no case where X = 0 Y (as X increases, Y has a tendency to increase)  Calculating the Terms of the Regression Line Formula o NEGATIVE CORRELATION – an increase in X is related to a decrease in ∑( ̅)( ̅) Y (as X increases, Y has a tendency to decrease)
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