Multiple Regression
Learning Objectives:
● Explain when you would use multiple regression analysis.
● Construct a multiple regression model to examine the association between one quantitative
outcome and two or more quantitative predictors
● Interpret the parameters in a multiple regression model
● Interpret the sums of squares in a multiple regression model
● Draw a conclusion about the explanatory power of two quantitative predictors of one
quantitative outcome.
● Explain how the parameter estimation and significance test of the multiple regression
model function.
(1) Hypothesis Testing
1.1 Process of Hypothesis Testing
1. Formulate an hypothesis
○ What do you expect?
2. Check study characteristics and variables
○ Sampling procedure, (experimental) design, measurement levels
3. Descriptive analyses
○ What are the sample characteristics, how are the relevant variables distributed (inc. M
and SDs)?
4. Inferential analyses
○ Test a relation or differences, including a check of the model diagnostics
5. Interpret and report results:
○ Report your findings in APA style
1.2 Hypotheses, Study Characteristics and Variables
Research Question: Do class size and percentage of free meals together explain differences in
academic performance?
Cross-sectional study across randomly selected schools in the Netherlands
3 Quantitative variables:
● Y: response variable (outcome variable) → academic performance
● X1 and X2: explanatory variables (predictor variable) → class size and percentage of free
meals (indicator of SES)
Hence, do class size and percentage of free meals together explain variation in academic
performance?
, 1.3 Bivariate Association
When an association between two variables is analysed
Academic performance and class size
● Positive association
● CS explained 11% of the variation in AP
Academic performance and percentage of free meals
● Negative association
● PFM explained 85% of the variation in AP
Class size and percentage of free meals
● Negative association
● PFM explained 12% of the variation in CS
Hence, how much variation in AP will PFM and CS
together explain?
Learning Objectives:
● Explain when you would use multiple regression analysis.
● Construct a multiple regression model to examine the association between one quantitative
outcome and two or more quantitative predictors
● Interpret the parameters in a multiple regression model
● Interpret the sums of squares in a multiple regression model
● Draw a conclusion about the explanatory power of two quantitative predictors of one
quantitative outcome.
● Explain how the parameter estimation and significance test of the multiple regression
model function.
(1) Hypothesis Testing
1.1 Process of Hypothesis Testing
1. Formulate an hypothesis
○ What do you expect?
2. Check study characteristics and variables
○ Sampling procedure, (experimental) design, measurement levels
3. Descriptive analyses
○ What are the sample characteristics, how are the relevant variables distributed (inc. M
and SDs)?
4. Inferential analyses
○ Test a relation or differences, including a check of the model diagnostics
5. Interpret and report results:
○ Report your findings in APA style
1.2 Hypotheses, Study Characteristics and Variables
Research Question: Do class size and percentage of free meals together explain differences in
academic performance?
Cross-sectional study across randomly selected schools in the Netherlands
3 Quantitative variables:
● Y: response variable (outcome variable) → academic performance
● X1 and X2: explanatory variables (predictor variable) → class size and percentage of free
meals (indicator of SES)
Hence, do class size and percentage of free meals together explain variation in academic
performance?
, 1.3 Bivariate Association
When an association between two variables is analysed
Academic performance and class size
● Positive association
● CS explained 11% of the variation in AP
Academic performance and percentage of free meals
● Negative association
● PFM explained 85% of the variation in AP
Class size and percentage of free meals
● Negative association
● PFM explained 12% of the variation in CS
Hence, how much variation in AP will PFM and CS
together explain?
