Correlation and Regression Lecture PDF

Correlation Correlational Research Designs  Example Murders Ice Cream  Example Murders Ice Cream Or… Murders Ice Cream  Correlation Variable X Variable Y Or… Variable X Variable Y Or...

Correlation Correlational Research Designs  Example Murders Ice Cream  Example Murders Ice Cream Or… Murders Ice Cream  Correlation Variable X Variable Y Or… Variable X Variable Y Or… Correlation: Variables X &Y Variable X Variable Y Or… Variable X Variable Y Or… Correlation: Variables: X, Y, & Z An unknown Variable Z is responsible for the relationship between Variables X&Y Variable X Variable Y Variable Z  Positive Correlation Variable X Variable Y  Positive Correlation Variable X Variable Y Negative Correlation Variable X Variable Y Negative Correlation Variable X Variable Y  Correlation With Correlation, we may never state that variable X causes a change in variable Y Likewise, we may never state that variable Y causes a change in variable X  Correlation With Correlation, we may never infer causation! There is never a cause & effect relationship with correlation  Correlation Acceptable terminology for use in a correlation: *Correlation between variables *Relationship between variables *Association between variables Never a difference between variables or a cause and effect relationship between variables  Pearson’s r Correlation rcalc = +number, positive correlation rcalc = -number, negative correlation rcalc = +1, a perfect positive correlation rcalc = -1, a perfect negative correlation rcalc = 0, no correlation at all rcalc must be between (-1 to +1)  Statistical Assessment of Relationships Pearson’s r – for quantitative dependent variables (interval & ratio) Spearman Rank Order Correlation Coefficient – for ordinal dependent variables Simple Linear Regression A Correlational Design  Simple Linear Regression Used for developing an equation that can be used for predicting the values of a specified Dependent Variable (DV). Simple Linear Regression uses one predictor variable and one dependent variable. X Predictor Variable Y Dependent Variable  Data with Scatterplot Exam I Exam II Person X Y 1 34 37 2 25 22 3 15 15 4 17 16  Scatterplot with Regression Line Exam I Exam II Person X Y 1 34 37 2 25 22 3 15 15 4 17 16  Simple Linear Regression The Linear Regression Formula is: Y = bX + a Where: b = slope of regression line a = where regression line intercepts the y axis (Y- Intercept) You may “plug-in” any score from the X-axis (X variable) to predict the score on the Y-axis (Y variable) Y = #X ± #