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SOCY211 Week 10, Lecture 2

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Queen's University
SOCY 211
Carl Keane

BIVARIATE REGRESSION - Allows us to make predictions - Ex. How much extra do you expect to earn by spending an extra year in the education system - LINEAR REGRESSION LINE/LEAST SQUARES LINE - When we look at a scatter graph you try to impose a straight line that fits the pattern of the dots o Called least squares line - (OLS - Ordinary Least Squares regression) - The Least Squares Line is the line that minimizes the sum of the squared distances between the line and the dependent variable score of each case. - Goal is to predict as accurately as possible - The distance is sometimes called the error or the residual - Regression Equation: Y = a + b (x) - Y = Dependent variable score that we want to predict - a = the value of Y where the regression line crosses the Y-axis. i.e. the value of Y when x is zero. (This is called Y Intercept or the constant.) - b = the change in the dependent variable (Y), for every one-unit change in the Independent Variable (X). (This is called the SLOPE, or sometimes the STEEPNESS of the line.) - x = the score on the Independent Variable - Hypothetical regression equation for Education (X) and Income (Y) a b Y = $5,000 + $1,000 (x) - a (Intercept) = $5,000 - this means that even with no education you will earn something ($5,000) - b = $1,000 - this means that, on average, every additional year in school will result in an additional $1,000 in income - x = Independent Variable score - this is the score we “plug” in. So, for example, we can predict that someone with 10 years of education will earn: Y = $5,000 + $1,000 (10) Thus: Y = $5,000 + $10,000 Thus: Y = $15,000 *You should always look at the scattered graph - regression line is the best predictor in general - you can break it up into samples of males and samples of females o suggest that the line is steeper for males than for females - there may be a possibility of earnings discrimination - similarly it can also be broken down into subgroups of whites and non whites 1 a b Males $5,000
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