## Lesson 7: Intro to Multiple Regression

February 11, 2019

Review:

- Exam 1 Results
- Exam 1 Solutions
- Retakes
- Portfolio Grading

Presentation:

- Intro to Multiple Regression
- y-hat = B0 + B1*x1 + B2*x2 + …. Bn*xn
- Multiple Regression with XL Miner and Statistics
- Simple Multiple Regression Demo (Sheets)
- Another demo with Sample Real Estate Data

- Write the linear equation for y-hat by hand

- Regression Output Interpretation
*t-statistics**p-values*- R² measures “goodness of fit” (explains % of variance)
- p-value measures “significance” (probability of result by chance)
- rank by significance

Activity:

- Use the “XL Miner” Add-on
- Complete Problems 1 and 2 using Sheets data
- Prob 1: Use “y” as dependent variable, use “x1”, “x2” and “x3” as independent variables
- Prob 2: Use “Dividend Payout” as dependent variable, use “Insider Ownership” and “Debt Ratio” as independent variables
- Highlight R-squared, coefficients, t-statistics and p-values
- Write the linear equation for y-hat by hand
- List, in rank order, the variables from most significant to least significant

- Run Multiple Regression using East Pueblo RE Sales 2014-2016
- Use “Selg Pr” (selling price) as dependent (y) variable, use “Bd”, “Ba”, “TtlGrSF”, and “DOM” as independent (x) variables
- Highlight R-squared, coefficients, t-statistics and p-values
- Write the linear equation for y-hat by hand
- List, in rank order, the variables from most significant to least significant

- Add Results to your Portfolio
- Include regression output with highlights
- y-hat equation (typed or hand-written)
- ranked list of independent variables from most to least significant