Multiple Regression– association between a criterion variable and two or more predictor variables (Aron & Aron, 2003).
Multiple correlation coefficient = R
Using two or more variables to predict a criterion variable.
Onwuegbuzie, A. J., Bailey, P, & Daley, C. E. (2000). Cognitive, affective, personality, and demographic predictors of foreign-language achievement. The Journal of Educational Research, 94 , 3-15. Foreign Language Achievement Cognitive Academic Ach. Study Habits Expectation Affective Perception Anxiety Personality Cooperativeness Competitiveness Demographic Gender Age
Espin, C., Shin, J., Deno, S. L., Skare, S., Robinson, S., & Brenner, B. (2000). Identifying indicators of written expression proficiency for middle school students. The Journal of Special Education, 34 , 140-153. Words written Words correct Characters Sentences Character/Word Word/sentences Correct word sentences Incorrect Word sentences Correct minus incorrect word sentences Mean length of correct word sentences Written Expression Proficiency
Regression coefficient ( ) / Beta weight – Distinct contribution of a variable, excluding any overlap with other predictor variables. Unstandardized simple regression coefficient
Standardized regression coefficient - converted variables (independent and dependent) to z-scores before doing the regression. Indicates which independent variable has most effect on the dependent variable.
“ The data were analyzed by multiple regression, using as regressors age, income and gender. The regression was a rather poor fit (R2adj = 40%), but the overall relationship was significant (F 3,12 = 4.32, p < 0.05). With other variables held constant, depression scores were negatively related to age and income, decreasing by 0.16 for every extra year of age, and by 0.09 for every extra pound per week income. Women tended to have higher scores than men, by 3.3 units. Only the effect of income was significant (t12 = 3.18, p < 0.01).