Bivariate Correlation and Regression

For Quantitative variables measured on the Interval Level Which one is the First? –Correlation or Regression

Objectives Scattergram Superimpose a regression line Estimate and interpret a correlation Estimate and interpret the regression coefficients Estimate and interpret Spearman’s rho

Scattergram

Sunflower

Regression Line What is the relationship between income and education? We need to know : –How much income you could expect to make if you had no education? –And how much income you can expect for each additional year of education Intercept or Constant Slope

Regression Line Estimated income = 10000$ $(Educ) Y=b 0 +b 1 (x 1 ) Predictor Outcome Constant

Correlation Measure how close the observations are to the regression line It does not tell us how steep the relation is

Think The correlation between education and income –Women : r = 0.3 –Men : r = 0.5 –Does this mean that education has a bigger payoff for men than it does for women?

Correlation Vary from -1 to 1 –It tell us whether the regression line goes up or down What r=0 means?

Multiple Comparisons

With Alpha adjustment

Approach to Missing Values Exclude cases pairwise Exclude cases listwise

Linear Regression Variable Selection Methods Enter (Regression) Stepwise Remove Backward Elimination Forward Selection

Non-Linear Associations