HRP 223 - 2008. Topic 9 - Regression. Height and Resting Pulse. The spreadsheet RESTING.xls has height and pulse measures on 50 people. On average, does pulse go up or down with height?. Look before you leap!. Root MSE = Estimated standard deviation of the error in the model (eta) - PowerPoint PPT Presentation
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The spreadsheet RESTING.xls has height and pulse measures on 50 people. On average, does pulse go up or down with height?
Look before you leap!
HRP223 2008
Root MSE = Estimated standard deviation of the error in the model (eta)
Dependent Mean = Mean of the outcome CV = ratio of above * 100 In general r2 is interpreted as:
– .1 small effect, 3. medium effect, .5 large effect Adjusted R-square =1- ( (1- rsquare) * ((n-1)/n-m-1)) )
n=subjects m=variables– It penalizes you for putting extra terms in the model.– R-squared is typically reported if you have a single predictor
variable.– Adjusted R-square is typically reported if you have several
predictors.
HRP223 2008
Oxygen
The next set of data looks at the relationship between oxygen inhaled and exhaled. You would hope that there would be close to a perfect relationship between the two factors.
Add the library to a new flowchart.
Add the SAS data set to the project.
Look at the Data This is bad news….
At least it is symmetric.
Simple correlation is questionable.
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Are the residuals about normal?
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Leave yourself a note on how to interpret the output.
Right click on the flowchart and choose New > Note. Leave yourself some notes. Right click on the Note icon > Link Note to > Quadratic
HRP223 2008
Ice cream!
In this example you will predict ice cream sales based on factors like price and temperature.
Start by making a library (or copy and paste the existing one) in a new flowchart.
The data is in a text file. Import the data.
Load the Data
Add Celsius
Celsius is ( (5/9) * (Fahr-32) ) 1
2
Celsius is ( (5/9) * (Fahr-32) )
HRP223 2008
Some people say VIF > 10 is a problem but that is arbitrary.
If VIF is > 1/(1 - R-squared) then the factors are more related to other predictors than outcome.
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Severely Dehydrated Children
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A Look
Do univariate descriptive statistics. – Things look reasonable.
Do bivariate correlations.– Age and weight are correlated
Do univariate modeling.– There is a weak but statistically significant
association. Build a model with all 3 predictors and check
variance inflation.
A Simpler Model
It explains a fair amount of the variability (45%). How can I check to make sure the model is working well and is not being driven by outliers?
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Outliers
Images from: Statistics I: Introduction to ANOVA, Regression, and Logistic Regression Course Notes (2005) and Categorical Data Analysis Using Logistic Regression Course Notes (2005), SAS Press.
First Check Residuals
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What is influential?
Freund and Littell SAS System for Regression 3rd edition, page 70;
Variance inflation:– vifcheck = 1 /(1 – r2)
Leverage greater than this value:– leverageCheck = 2 * (predictors + 1) / records