The Idea of Linear Regression

2 • Linear and other regression modeling – What does it mean to model? – What are the assumptions? – What should I ask during a briefing? Goals for this Lecture 3On to Model Building! • Up to now, we’ve discussed descriptive and inferential statistics – Numerical and graphical summaries of data – Confidence intervals – Hypothesis testing • Can apply those tools and build models to try to explain data – For each “Y ” in my data I also observe an “X” – Can I use X to say something about Y? 4Why Model? • Raw data by itself (pairs of X and Y) often too hard to interpret • Scatter plots informative, but can also sometimes have too much information • Linear regression models the relationship between X and Y via a linear equation • General expression for a linear equation: – 1 is the slope (change in Y for a unit change in X) – 0 is the intercept (value of Y when X =0) XY o