## Lesson 4: Intro to Multiple Regression

January 24, 2018

Review:

- Simple Regression
- Submit Assignment

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-statistic**p-value*- R² measures “goodness of fit” (explains % of variance)
- p-value measures “significance” (probability of result by chance)
- rank by significance

Assignment:

- Use “Statistics” or “XL Miner” Add-on, your choice
- 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

- Prepare a 1-page summary
- Include regression output with highlights
- y-hat equation (typed or hand-written)
- ranked list of independent variables from most to least significant

- Submit in class on Monday