1. Model Regress Linear 3Factor Excel 2013 V0F 1 by Milo Schield Member: International Statistical Institute US Rep: International Statistical Literacy Project Director, W. M. Keck Statistical Literacy Project Slides at: www.StatLit.org/pdf /Model-Regress-Linear-3Factor-Excel2013-6up.pdf /Model-Regress-Linear-3Factor-Excel2013-1up.pdf Model using Regress Linear 3Factor in Excel 2013

2. Model Regress Linear 3Factor Excel 2013 V0F 2 Goal: Summarize association before/after control for Gender Required output: Create and upload your worksheet*: 1. Generate two charts (slides 4 and 15). Slide 4: Show trend-line, equation and R 2. Slide 15: Show trend-lines. Show regression model. 2. Generate/show averages (slide 3). 3. Generate/show output from regression (slide 9). Data: www.StatLit.org/xls/Pulse-Regress-Worksheet.xlsx Note: Male is already in column D in this worksheet. Demo output: www.StatLit.org/pdf/Pulse-Regress-Output.pdf Subjects are college students. Male: 1 for men; 0 for women.

3. Model Regress Linear 3Factor Excel 2013 V0F 3 Analyze Data: Enter Formula into K3:L4 Actual male-female differences: Average weight: 158.3 - 123.8 = 34.5 pounds Average height: 70.75 – 65.40 = 5.35 inches Question: How much of the male-female weight difference (34.5#) is due to gender (male vs. female) and how much is due to the difference in heights? Analyzing a whole into parts is called “decomposition”.

4. Model Regress Linear 3Factor Excel 2013 V0F 4 Chart #1.

5. Model Regress Linear 3Factor Excel 2013 V0F 5 Decompose Male-Female Weight Difference: 1 st try Actual male-female differences (slide 3): Average weight: 158.3 - 123.8 = 34.5 pounds Average height: 70.75 – 65.40 = 5.35 inches Model Weight on Height (slide 4) Expected Weight = -204.74 + 5.09 * Height Decomposition of male-female weight difference: Due to Height difference: 5.09*5.35 = 27.23# Due to Sex (Gender) difference: 34.5# – 27.2# = 7.3# Inadequate!!! Sex and height are confounded in slope.

6. Model Regress Linear 3Factor Excel 2013 V0F 6 Model Weight by Height & Sex: Four Step Process Step 1. From Data Toolbar, select Data Analysis (in the Analysis section). Select Regression Step 2. Regress Weight on Height and Gender Step 3. Generate Y values given X for models Step 4. Generate two trend lines on XY plot

7. Model Regress Linear 3Factor Excel 2013 V0F 7 1) Data Toolbar, select Data Analysis. Select Regression.

8. Model Regress Linear 3Factor Excel 2013 V0F 8 2a) Regress Weight on Height and Sex.

9. Model Regress Linear 3Factor Excel 2013 V0F Weight = -117.6 + (3.69*Height) + (14.7*Male). 9 2b) Results: Regress Weight on Height and Sex (Male?) Formatting and formula are optional

10. Model Regress Linear 3Factor Excel 2013 V0F 10 3) Expected Weights at selected Heights for Men and Women Create formula in L33 predicting weight: Pull L33 down

11. Model Regress Linear 3Factor Excel 2013 V0F 11 4a) Start with new chart: Select Data; Select “Add”.

12. Model Regress Linear 3Factor Excel 2013 V0F 12 4b) Add Two New Series.

13. Model Regress Linear 3Factor Excel 2013 V0F 13 4c) After Adding Two New Series, Press “OK”.

14. Model Regress Linear 3Factor Excel 2013 V0F 14 4d) Select Data Point. Format Data Series. Select ‘Solid Line’.

15. Model Regress Linear 3Factor Excel 2013 V0F 15 4e) Add Regression Equation. Final Result.

16. Model Regress Linear 3Factor Excel 2013 V0F 16 Decompose Male-Female Weight Difference: 2 nd try Multivariate ‘regression’ model (slide 9 or 15): Weight = -117 + (3.7*Height) + (14.7*Male) Difference in average heights: 5.35” (slide 3) Difference in average weights: 34.5# (slide 3) 14.7 pounds due to gender difference – after controlling for height. 19.8 pounds due to height difference – after controlling for gender: 3.7 #/inch * 5.35 inches Moral: How you take things into account matters!

17. Model Regress Linear 3Factor Excel 2013 V0F 17 Decompose Male-Female Weight Difference: Summary Decompose 34.5# male-female weight difference. 1 st try: Regress weight on height (R 2 =.62) 27.2 pounds due to height difference 7.3 pounds due to gender difference Problem: Gender, height and weight are confounded 2 nd try: Regress weight on height and sex (R 2 =.66) 19.8# due to height – after controlling for gender 14.7# due to gender – after controlling for height Moral: How you take things into account matters!