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Model Trendline Linear Excel 2013V0F 1
byMilo 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
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Model Trendline Linear Excel 2013V0F 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 R2: the goodness of fit.
3. Describe the trend (qualitatively and quantitatively) in words for each graph.
4. [Optional] Describe the associated model in words.
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Model Trendline Linear Excel 2013V0F 3
Approach: Data Selection
Three approaches to selecting data1. Select X and Y axis data before inserting chart2. Select just the Y-axis data before inserting chart3. 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.
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Model Trendline Linear Excel 2013V0F 4
#1 Select columns (Ht & Wt)Insert Scatter (XY) chart
.
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Model Trendline Linear Excel 2013V0F 5
Excel does this automatically
Do not include row 1; Excel translates text to zero.
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Model Trendline Linear Excel 2013V0F 6
First ChartNext: Remove white space
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Model Trendline Linear Excel 2013V0F 7
Format X Axis
Point at horizontal axis; Press right mouse; Select “Format Axis”
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Model Trendline Linear Excel 2013V0F 8
Format X Axis
Change Minimum from zero to 60
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Model Trendline Linear Excel 2013V0F 9
Format X Axis: Result
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Model Trendline Linear Excel 2013V0F 10
Format Y Axis:
Point at vertical axis; Press right mouse; Select “Format Axis”
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Model Trendline Linear Excel 2013V0F 11
Format Y Axis: Result
Change Minimum from zero to 90
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Model Trendline Linear Excel 2013V0F 12
Insert Trend-line & Formulas
Select Chart Elements
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Model Trendline Linear Excel 2013V0F 13
Insert Trend-line & Formulas
Check “Trendline” (Linear is default); Select “More Options”
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Model Trendline Linear Excel 2013V0F 14
Insert Linear Equation and R2
Scroll Down
Check “Display Equation”; Check “Display R-squared value”
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Model Trendline Linear Excel 2013V0F 15
Edit Headings; Chart Result
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Model Trendline Linear Excel 2013V0F 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)
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Model Trendline Linear Excel 2013V0F 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.
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Model Trendline Linear Excel 2013V0F 18
#2 Select Pulse1 (Y-axis) Insert Scatter (XY) chart
.
Select data. Edit data.
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Model Trendline Linear Excel 2013V0F 19
#2 Select Data; Edit Series; Insert X-Axis Range
.
Do not include the heading row
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Model Trendline Linear Excel 2013V0F 20
Format Axis and Title. Add Trendline, Equation and R2
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Model Trendline Linear Excel 2013V0F 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]
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Model Trendline Linear Excel 2013V0F 22
#3: Duplicate previous graph with Height on X-Axis
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Model Trendline Linear Excel 2013V0F 23
Describe Slope and Fit[Model is optional]
Review and modify the description given on slide 21.
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Model Trendline Linear Excel 2013V0F 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 (R2 < 5%)
of resting pulse (Pulse1)Height is a fair predictor (R2 ~ 60%) of weight.