1. Model Trendline Linear 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-Trendline-Linear-Excel2013-6up.pdf Model using Trendline (Linear) in Excel 2013

2. Model Trendline Linear Excel 2013 V0F 2 Goal: Summarize association between two variables 1.Create three charts showing the association between two quantitative variables. See slides 15, 20 and 22. 2.Show trend-line for the association. Show the equation and R 2 : the goodness of fit. 3.Describe the trend (qualitatively and quantitatively) in words for each graph. 4.[Optional] Describe the associated model in words.

3. Model Trendline Linear Excel 2013 V0F 3 Approach: Data Selection Three approaches to selecting data 1.Select X and Y axis data before inserting chart 2.Select just the Y-axis data before inserting chart 3.Select X and Y axis data after inserting chart. Evaluation: #1: best if X-axis data is to the left of Y-axis data #2: best if X-axis data is to the right of Y-axis data #3: allows the most control.

4. Model Trendline Linear Excel 2013 V0F 4 #1 Select columns (Ht & Wt) Insert Scatter (XY) chart.

5. Model Trendline Linear Excel 2013 V0F 5 Excel does this automatically Do not include row 1; Excel translates text to zero.

6. Model Trendline Linear Excel 2013 V0F 6 First Chart Next: Remove white space

7. Model Trendline Linear Excel 2013 V0F 7 Format X Axis Point at horizontal axis; Press right mouse; Select “Format Axis”

8. Model Trendline Linear Excel 2013 V0F 8 Format X Axis Change Minimum from zero to 60

9. Model Trendline Linear Excel 2013 V0F 9 Format X Axis: Result

10. Model Trendline Linear Excel 2013 V0F 10 Format Y Axis: Point at vertical axis; Press right mouse; Select “Format Axis”

11. Model Trendline Linear Excel 2013 V0F 11 Format Y Axis: Result Change Minimum from zero to 90

12. Model Trendline Linear Excel 2013 V0F 12 Insert Trend-line & Formulas Select Chart Elements

13. Model Trendline Linear Excel 2013 V0F 13 Insert Trend-line & Formulas Check “Trendline” (Linear is default); Select “More Options”

14. Model Trendline Linear Excel 2013 V0F 14 Insert Linear Equation and R 2 Scroll Down Check “Display Equation”; Check “Display R-squared value”

15. Model Trendline Linear Excel 2013 V0F 15 Edit Headings; Chart Result

16. Model Trendline Linear Excel 2013 V0F 16 Describe Slope and Fit [Model is optional] Slope (Qualitative): Taller people weigh more [than shorter people] As height increases, weight increases (a positive association). Slope (Quantitative): As height increases by 1 inch, weight increases by 5.1 pounds. Weight increases by 5.1 pounds for every 1” increase in height. Quality of the Model (Fit) using R-squared 62% of the variation in weight is explained by height. Linear model of Weight based on Height: [Optional] Predicted weight = (5.1#/inch)*Height(inches) – 240# Mean height is 65”; Mean weight is 150#. Predicted weight = AveWt + (5.1#/inch)(Ht – AveHt)

17. Model Trendline Linear Excel 2013 V0F 17 Optional: Use model to predict your weight using your height Formula applies to college students but is not based on a random sample. Formula does not distinguish Gender, Race, Ethnicity or Age Fitness, metabolism, body build or medical status. ======================================= Assume a height of 66 inches. Predicted weight = -205 # + 66 inches * 5.1 # per inch = 336 – 205 = 131 pounds.

18. Model Trendline Linear Excel 2013 V0F 18 #2 Select Pulse1 (Y-axis) Insert Scatter (XY) chart. Select data. Edit data.

19. Model Trendline Linear Excel 2013 V0F 19 #2 Select Data; Edit Series; Insert X-Axis Range. Do not include the heading row

20. Model Trendline Linear Excel 2013 V0F 20 Format Axis and Title. Add Trendline, Equation and R 2

21. Model Trendline Linear Excel 2013 V0F 21 Describe Slope and Fit [Model is optional] Slope (Qualitative): Heavier people have lower rest pulse rate [than lighter people] As weight increases, rest pulse decreases (negative association) Slope (Quantitative): As weight increases by 10#, rest pulse decreases by 0.9 BPM. Rest pulse decreases by 0.9 bpm for every extra 10# in weight. Quality of the Model (Fit) using R-squared 4% of the variation in rest pulse is explained by weight. Linear model of Rest Pulse based on Weight: [Optional] Predicted rest pulse = [-0.094 bpm/#]*Weight(#) + 86.5 bpm Mean rest pulse is 67 bpm; Mean weight is 150#. Predicted weight = AveWeight + [5.1#/inch][Height – AveHt]

22. Model Trendline Linear Excel 2013 V0F 22 #3: Duplicate previous graph with Height on X-Axis

23. Model Trendline Linear Excel 2013 V0F 23 Describe Slope and Fit [Model is optional] Review and modify the description given on slide 21.

24. Model Trendline Linear Excel 2013 V0F 24 Comparison of Models R-squared: quality of the model. 62% of weight variation is explained by height 4.1% of Pulse1 variation explained by Weight 4.5% of Pulse1 variation explained by Height Conclusions: Height and weight are poor predictors (R 2 < 5%) of resting pulse (Pulse1) Height is a fair predictor (R 2 ~ 60%) of weight.