Title 4.4. Regression and Conditional Conditional Means.pdf ✅

pacmann.io © 2022 – Pacmann AI 31 Regression
pacmann.io © 2022 – Pacmann AI 32 Revisiting Ordinary Least Square ● Ordinary least squares (OLS) or linear regression is another way to summarize the relationship between variables using linear function. ● One of simplest form of OLS can be visualized as a straight line ● Easy interpretation: a one-unit change in X is associated with a β1-unit change in Y *If we’ve identified a causal effect then a one-unit change in X causes a β1-unit change in Y
pacmann.io © 2022 – Pacmann AI 33 ● This function tells us that the mean of Y conditional on X, say, when X is 3, Y is 23. ● It also tells us that the mean of Y conditional on a given value of X would be 6 higher if you instead made it conditional on a value of X one unit higher. OLS : Example 1
pacmann.io © 2022 – Pacmann AI 34 ● Dataset of women’s labor force participation and earnings from 1975. ● wg: Women wage rate in family. ● inc: Family income exclusive of wife's income OLS : Example 2