


Sherril M. Stone, Ph.D. 

Department of Family Medicine 

OSUCollege of Osteopathic Medicine 





Correlation Ð statistical technique that
describes degree of relationship between 2 variables 

Regression Ð technique that uses data to write
an equation for a straight line. 

The equation then is used to make some type of prediction
of the data. 

Draw a line of best fit (straight line) 

Make prediction of 2nd score when 1st score is
known 

Linear regression  from the phenomenon of
regression toward the mean, a consequence of the laws of probability when
correlation is less than perfect (as correlation gets lower, prediction
gets closer to z = 0). 




Slopeintercept formula for a straight line is 



Y = mX + b 



Y and X = variables (scores) on the Y and X
axes 

m = slope of the line (a constant) 

b = intercept (intersection) of line with Y
axis 

Positive Ð highest point on line is Right of
lowest point 

Negative Ð highest point on line is Left of
lowest point 

Equal Ð horizontal lines 

Large (+ or ) Ð vertical lines 




Regression Equation Formula Ð finds the line of
best fit 

Least squares method (LSM)ÐPearsonÕs mathematics
to create a straight line. LSM produces a value for the slope and the
intercept. With slope and intercept Ð write an equation for a straight line
(this is one that best fits your data) 



Ŷ = a + bX 



Ŷ = predicted value of Y from X 



a = point where line intersects Y axis a, b =
regression 

b = slope of the regression line
coefficients 

X = X score (data) used to predict Y 






Correlation coefficient (r) Pearson productmoment correlation
Ð measures the degree and
direction of linear relationship between 2 variables 

Coefficient of determination (r^{2}) Ð
proportion of shared variance (s^{2}) between 2 variables 

Effect size for r Ð Small
.10 

Med .30 

Large .50 




Blanched formula 

ŒXY 

Ð (X)(Y) 

r = N 

(SD_{X})(SD_{Y}) 

Raw score formula 

NŒXY Ð (ŒX)( ŒY) 

r = 

… (NŒX^{2} Ð (ŒX)^{2} (NŒY^{2} Ð (ŒY)^{2} 




SD_{Y} 

b = r SD_{X} 



 OR  



NŒXY Ð (ŒX) (ŒY) 

b = 

N ŒX^{2}
Ð (ŒX)^{2} 




Calculate mean and SD 

Calculate r and r^{2} 

Calculate b 

Calculate a 

Predict Y 




X X2 Y Y2 XY 

5 3 

7 4 

1 1 

6 3 

9 5 

9 5 

10 7 

4 3 

3 2 

2 2 

·X ·Y 

N = 

SD_{X} r = 

SD_{Y} r^{2} = 

b = 

a = 

Ŷ = a + bX 




X X2
Y Y2 XY 

21 8 

14 9 

16 10 

11 15 

15 11 

10 16 

9 14 

8
21 

·X ·Y 

N = 

SD_{X} r = 

SD_{Y} r^{2} = 

b = 

a = 

Ŷ = a + bX 

