Multiple Regression Research Methods and Statistics

Intended Learning Outcomes  At the end of this lecture and with additional reading you will be able to describe principles of a regression analysis describe assumptions of regression analysis describe the principles of the regression equation

Perfect Positive Relationships  Scattergrams: all the datapoints fall on a straight line every time your sister ages by one year, so do you no cause can be attributed to correlational analysis

Perfect Negative Relationships  Points will fall on a straight line: everytime x increases by a certain amount, y decreases by a certain, constant amount

The Strength/magnitude of the Relationship  The strength of the relationship goes from zero to +1 (for positive relationships)  and zero to -1 (for negative relationships  Correlations are often given to two places, e.g zero

Regression  Regression is an extension of a correlation. It allows you to predict the impact of one variable against another: bivariate linear regression assess one variable against another multiple regression assess several variables against another

Assumptions of regression  Multicolinerarity  Homoscedasticity  Outliers  Independence  linearity  Normal distribution  Large sample (15+ per variable)

Regression analysis  In regression variables are classed as criterion (DV’s) or predictors (IV’s) regression will show the amount of a change in y as a results of change in x (regression equation) it therefore allows researchers to predict scores of y against changes in x

Regression analysis  For linear regression we can calculate someone's score on y from their score on x y = bx + a y is the variable to be predicted x is the score on variable x b is the value for the slope of the line a is the value of the constant (that is where the the straight line intercepts the y axis, also called the intercept)

For example  If we think back to our study on stress in the police service, suppose we want to predict the anxiety scores from the depression scores remember y = bx + a y = 1.1 x y = 35.3

Multiple regression  Multiple regression is an extension of linear regression  It enables researchers to assess several predictor variables against a criterion variable

 The multiple regression equation allows all predictor variables to contribute to the outcome of the criterion variable  Therefore if we were trying to predict scores on anxiety from depression and dissociation score we would use the following equation: y = b¹x¹ + b²x² + b³x³ …. + a y = 1 x x y = 36.03

Output terminology  R: the correlation coefficient  R squared: the amount of variance explained  Adjusted r: the variance explain adjusted to give a more realistic estimate  Standard error: the standard deviations of the amount of error that may occur  ANOVA: whether the regression line is significantly different from o  B and Beta values: B values are the slope of the line and Beta are standardized coefficients and advise the strength of the predictor