Correlation and Regression. Slides by Brad Evanoff, MD, MPH Talk by Brian Gage, MD, MSc. Overview of Correlation and Regression. Correlation seeks to establish whether a relationship exists between two variables Regression seeks to use one variable to predict another variable
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Correlation seeks to establish whether a relationship exists between two variables
Regression seeks to use one variable to predict another variable
Both measure the extent of a linear relationship between two variables
Statistical tests are used to determine the strength of the relationship
Scatterplot F shows the relationship between temperature and number of nerve fiber discharges
The scatterplot demonstrates a strong relationship
However, the correlation coefficient, which only measures a linear relationship, has a value of zero (Note that scatterplot E also has an r value of zero but clearly no relationship exists between the two variables)
Type of Data
Continuous v.
Continuous
Continuous v.
Ordinal
Ordinal v.
Ordinal
Correlation Coefficient
Pearson’s r
Jaspen’s Multiserial
Coefficient (M)
Spearman’s r (Rho)
Kendall’s t (Tau)
Because the points rarely fall along a perfect straight line, there is also an error term e
Y´= 1.61 + 0.406X, where Y´ is the predicted MCAT score and X is the ACT score
R = 0.62
Y = estimated value for dependent (outcome) variable
ß0 = intercept
ß1= partial regression coefficients: indicate how much Y changes for each unit of change in X, when all other variables in the model held constant
Xi = independent (predictor) variables
Table. Multivariate Analysis: Independent Predictors of Warfarin Dose
Entry into Model
Variable
Coefficient
Change in Warfarin Dose, % (95% CI)
P value
0
Intercept
+0.404


1
Age, per decade
–0.0084
–8 (–5 to –11)
<0.001
2
BSA, per SD
+0.50
+14 (+8 to +18)
<0.001
3
SNPs, per allele
–0.25
–22 (–16 to –28)
<0.001
4
Amiodarone
–0.34
–29 (–16 to –40)
0.001
5
Target INR, per 0.5 increase
+0.38
+21 (+9 to +34)
<0.001
6
Simvastatin
–0.13
–13 (–2 to –22)
0.03
7
White race
–0.123
–12 (–3 to –20)
0.01