HRP 223 - 2008 Topic 9 - Regression
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maximum extent possible under the law. Height and Resting Pulse HRP223 2008
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.
Oxygen HRP223 2008
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.
HRP223 2008 Are the residuals about normal?
Leave yourself a note on how to interpret the output. HRP223 2008
Right click on the flowchart and choose New > Note. Leave yourself some notes. Right click on the Note icon > Link Note to > Quadratic
Ice cream! HRP223 2008
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
2 Add Celsius Celsius is ( (5/9) * (Fahr-32) )
1 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 - Rsquared) then the
factors are more related to other predictors than outcome.
Severely Dehydrated Children HRP223 2008
A Look Do univariate descriptive statistics. HRP223 2008
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?
Outliers HRP223 2008
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 What is influential? HRP223 2008
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 Covariance more extreme than:
cov1Check = 1 + 3 * (predictors+1) / records cov1Check = 1 - 3 * (predictors+1) / records Dfits values with absolute value bigger than:
dffitsCheck = 2 * ((predictors + 1)/records) ** .5 Influence Code HRP223 2008
