STAT 301 Lab

Lab 10: Least Squares Regression

T.A.: Yixuan Qiu

Scatterplot

• Study the relationship between two quantitative variables.

Scatterplot

• Form: linear or non-linear?
• Direction: positive or negative?
• Strength: strong or weak?
• Outliers?

Linear Regression

• Find a straight line to fit the relationship between $X$ and $Y$
• Also used to predict $Y$ for a given $X$

Regression Equation

• $\hat{y}=b_0+b_1 x$

Check the Assumptions

• Data coming from SRS
• Variables linearly related (Scatterplot)
• Normality of $Y$ (PP-plot)
• Same standard deviation at all $X$ values (Residual plot)

PP-plot

Residual Plot

• Residual = $y$ - $\hat{y}$