Linear regression

Slides

• “Linear regression”
• “Least squares estimation”
• “Adding covariates”
• “Least squares estimators”
• “Correlation and regression”
• “Hypothesis testing on regression parameters”
• “Adding more covariates”
• “Adding interactions between variables”
• “Nonlinear linear regression”

Control questions:

• What is the interpretation of \(\beta_0\) is a simple linear regression \(Y=\beta_0+\beta_1 X+\epsilon\)?
• What is the interpretation of \(\beta_1\)?
• What are we minimizing when estimating \(\beta_0\) and \(\beta_1\)?
• When is there a one-to-one relationship between the correlation between \(X\) and \(Y\) and the regression coefficient for \(X\)?
• What is the null hypothesis when we are looking at the default table from a linear regression in Python?
• If \(\text{Height_i}=\beta_0+\beta_a \text{Age}_i + \beta_m\text{Male}_i+\epsilon_i\), where \(\text{Male}_i\) is 1 if the child is male, what is the intercept for male and females?
• If \(\text{Height_i}=\beta_0+\beta_a \text{Age}_i + \beta_m\text{Male}_i+\beta_{a\times m}\text{Age}_i\text{Male}_i+\epsilon_i\), where \(\text{Male}_i\) is 1 if the child is male, what is the slope for male and females?
• How can we implement a nonlinear relations in a linear regression?