L1.pdf - APPLIED STATISTICS Simple Linear Regression and Its Estimation Dr Tao Zou Research School of Finance Actuarial Studies Statistics The

L1.pdf - APPLIED STATISTICS Simple Linear Regression and...

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APPLIED STATISTICS Simple Linear Regression and Its Estimation Dr Tao Zou Research School of Finance, Actuarial Studies & Statistics The Australian National University Last Updated: Wed Aug 2 08:35:02 2017 1 / 18
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Overview Introduction to Simple Linear Regression (SLR) SLR Model Assumptions Estimation of SLR Model 2 / 18
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References 1. F.L. Ramsey and D.W. Schafer (2012) Chapter 7 of The Statistical Sleuth 2. The slides are made by R Markdown . 3 / 18
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Simple Linear Regression Simple linear regression (SLR) is used to describe the mean of the response , as a function of a single explanatory variable . For example: using a person’s height (explanatory) to predict his/her weight (response), or using lean body mass (explanatory) to predict muscle strength (response). 4 / 18
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What is a response variable? 5 / 18
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Example: Old Faithful Old Faithful is a cone geyser located in Yellowstone National Park in Wyoming, United States. "oldfaithful.csv" DURATION (explanatory): Duration of Old Faithful Eruptions (mins). INTERVAL (response): Interval until Subsequent Eruption (mins). 6 / 18
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R Code rm ( list= ls ()) setwd ( ~/Desktop/Research/AppliedStat2017/L1 ) oldfaith<- read.table ( "oldfaithful.csv" , header= T, sep= "," ) plot (oldfaith$DURATION,oldfaith$INTERVAL, ylab= "Interval (mins)" , xlab= "Duration (mins)" , main= "Old Faithful Data" ) fit<- lm (oldfaith$INTERVAL~oldfaith$DURATION) abline (fit) 2.0 2.5 3.0
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