Lecture 4: Multiple Regressions
Multiple regression: used when there is more than one numeric independent predictor and a numeric
dependent variable
Purpose :
Test hypotheses about associations between numeric variables
Predict new values of a dependent variable based on values for independent variable(s)
Assumptions
Residuals are normally distributed —> QQplot
Linear relationships between dependent and independent variables —> scatterplot
No Multicollinearity (high correlations between independent variables)
Makes it difficult to interpret and testing significance of coefficients
Correlation should not be > 0.80
Homoscedacity
Simple linear regression
i is each case (baby) in the sample
Yi is the independent variable (weight)
a is the constant/intercept ( weight if 0 weeks gestation)
b is the slope of the regression line (increase in weight per week gestation)
ei is the error (difference between observed weights and predicted weights based on the linear model)
Linear regression in R:
Multiple Regression:
Multiple regression: used when there is more than one numeric independent predictor and a numeric
dependent variable
Purpose :
Test hypotheses about associations between numeric variables
Predict new values of a dependent variable based on values for independent variable(s)
Assumptions
Residuals are normally distributed —> QQplot
Linear relationships between dependent and independent variables —> scatterplot
No Multicollinearity (high correlations between independent variables)
Makes it difficult to interpret and testing significance of coefficients
Correlation should not be > 0.80
Homoscedacity
Simple linear regression
i is each case (baby) in the sample
Yi is the independent variable (weight)
a is the constant/intercept ( weight if 0 weeks gestation)
b is the slope of the regression line (increase in weight per week gestation)
ei is the error (difference between observed weights and predicted weights based on the linear model)
Linear regression in R:
Multiple Regression:
