May 9 - May 9 2008 Bivariate correlation and regression...

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May 9, 2008 Bivariate correlation and regression Correlation o A measure of the strength of the relationship between X and Y o It varies from -1 (a perfect negative relationship) to 1 (a perfect positive relationship) o It tells us how closely to our regression line the points cluster Calculating the correlation o We don’t have to calculate this formula (so I didn’t write it down) The coefficient of determination o R 2 o The proportion of the variance in the dependent variable that is explained by the independent variable o It ranges from 0 to 1.0 More on the regression line o The correlation can’t tell us how to predict Y based on X – we need the regression line o Called a “least squares” regression line Minimizes squared distances between each point and the line o Population: y = α + βx o Sample : y(dependent variable) = a +b(x[independent variable]) The slope/regression coefficient o B is the slope, or regression coefficient
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Unformatted text preview: o It tells us change in y that corresponds to x increasing by 1 o B = (Σ ( x - ) ( y - )) / (Σ (x - ) 2 ) The y-intercept o This is α, or a (for a sample) o It is the value of y when the line crosses the y-intercept (when x=0) o After we find b, then we know that a = Y – b X o If X = 14.4, Y = 4.6, and b =1.4 a = 4.6 – (1.4)14.4 = -15.6 Using the regression line for predictions o Since y = a + b(x), we can predict y if we know b and a If a =10, and b = 2, what is the predicted value of y when X=15? Y = 10 +2(15) = 40 o In the example of age and delinquency: a = -15.6; b = 1.4; r = .87; r 2 = .75 If X = 15, what is the predicted value of Y? Y = -15.6 + (1.4)15 = -15.6 + 21 = 5.4 Does this fit the scatter plot value? About right How much of the variance is explained?...
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  • Spring '09
  • Kupchick
  • Regression Analysis, regression line, perfect negative relationship, perfect positive relationship

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