May 9 - o It tells us change in y that corresponds to x...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern