Regression

Qualitative Predictors Predictors with Only Two Levels Suppose that we wish to investigate differences in credit card balance between males and females, ignoring the other variables for the moment. If a qualitative predictor (also known as a factor) only has two levels, or possible values, then incorporating it into a regression model is very simple. We simply create an indicator or dummy variable that takes on two possible numerical values. and use this variable as a predictor in the regression equation. This results in the model ...

Simple Linear Regression Models Linear Regression Model Form of the linear regression model: $y=\beta_{0}+\beta_{1}X+\epsilon$. Training data: ($x_1$,$y_1$) … ($x_N$,$y_N$). Each $x_{i} =(x_{i1},x_{i2},…,x_{ip})^{T}$ is a vector of feature measurements for the $i$-th case. Goal: estimate the parameters $β$ Estimation method: Least Squares, we pick the coefficients $β =(β_0,β_1,…,β_p)^{T}$ to minimize the residual sum of squares Assumptions: Observations $y_i$ are uncorrelated and have constant variance $\sigma^2$; $x_i$ are fixed (non random) The regression function $E(Y |X)$ is linear, or the linear model is a reasonable approximation. ...