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HRP 223 - 2008

Topic 9 - Regression

HRP223 2008

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!

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

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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) )

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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

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

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Influence Code