Chapter5

Chapter5 - Chapter 5 SAS Chapter 5 Correlation and...

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Chapter 5 SAS - 1 - Chapter 5 Correlation and Regression Analysis In this chapter, we will introduce how to compute correlation and perform regression analysis. 5.1 Correlation 1. PROC CORR (BASE SAS) a. Finds the estimated correlation between variables. Usually, correlation is denoted by “r” . i. -1 r 1 ii. Closer to 1, the stronger the positive relationship (as X , Y ) iii. Closer to -1, the stronger the negative relationship (as X , Y ) iv. Closer to 0, the weaker the relationship between X and Y b. The formula for the estimated Pearson correlation is: c. Options in the PROC CORR line i. Different types of correlations can be found. By default, Pearson correlation statistics are computed from observations with nonmissing values for each pair of analysis variables. we will only discuss the Pearson correlation ii. COV – finds the covariance matrix iii. OUTP=___ - creates a data set containing the Pearson correlations d. VAR statement – put variables of interest here 2. A simple example Let us revisit the SASDATA.Adjcereal data set. We would like to find the correlations among the nutrition variables *Find the correlation matrix using PROC CORR; title2 'Correlations among the nutrition variables' ; proc corr data =sasdata.Adjcereal outp =out_set1; var sugar fat sodium; run ;
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Chapter 5 SAS - 2 - Correlations among the nutrition variables The CORR Procedure 3 Variables: sugar fat sodium Simple Statistics Variable N Mean Std Dev Sum sugar 40 0.28942 0.14956 11.57662 fat 40 0.03218 0.02769 1.28731 sodium 40 5.61470 2.46253 224.58815 Simple Statistics Variable Minimum Maximum sugar 0 0.55556 fat 0 0.09259 sodium 0 10.71429 Pearson Correlation Coefficients, N = 40 Prob > |r| under H0: Rho=0 sugar fat sodium sugar 1.00000 0.23972 -0.16357 0.1363 0.3132 fat 0.23972 1.00000 -0.06614 0.1363 0.6851 sodium -0.16357 -0.06614 1.00000 0.3132 0.6851 a. Interpretation of the output: i. The estimated correlation between sugar and fat is r = 0.23972. ii. The p-value for a hypothesis test of H o : Population correlation = 0 (no correlation) H a : Population correlation 0 (positive or negative correlation) is 0.1363. Thus, do not reject H o . There is not enough evidence to conclude a significant correlation between sugar and fat. b. Print of the data out_set1:
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Chapter 5 SAS - 3 - Correlations among the nutrition variables Obs _TYPE_ _NAME_ sugar fat sodium 1 MEAN 0.2894 0.0322 5.6147 2 STD 0.1496 0.0277 2.4625 3 N 40.0000 40.0000 40.0000 4 CORR sugar 1.0000 0.2397 -0.1636 5 CORR fat 0.2397 1.0000 -0.0661 6 CORR sodium -0.1636 -0.0661 1.0000
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Chapter 5 SAS - 4 - 5.2 Regression Analysis Review Regression analysis is the analysis of the relationship between a response or outcome variable and another set of variables. The relationship is expressed through a statistical model equation that predicts a response variable (also called a dependent variable or criterion ) from a function of regressor variables (also called independent variables, predictors, explanatory variables, factors, or carriers ) and parameters . In a linear regression model the predictor function is linear in the parameters (but not necessarily linear in the regressor variables). The parameters are estimated so that a measure of fit is optimized.
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This note was uploaded on 06/06/2011 for the course STAT 4360 taught by Professor Park during the Spring '11 term at UGA.

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Chapter5 - Chapter 5 SAS Chapter 5 Correlation and...

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