Chapter 14. Correction and Simple Linear
Regression
•Scatter Diagram: A two-dimensional graph on which each observation in
the sample of bivariate data is represented by a point (dot).
•Negative (inverse) Relationship: A relationship between two variables, X
and Y, in which large values of X are associated with small values of Y.
•Positive (direct) Relationship: A relationship betwee two variables, X
and Y, in which large values of X are associated with large values of Y.
•Coefficient of Correlation (r): A statistical measure of the strength of
the linear relationship between two variables, calculated from a sample of
bivariate data. It is an estimate of the population coefficient of correlation.
r=P(x−x)(y−y)
pP(x−x)2P(y−y)2=SCPXY
√SSX√SSY
.
−1≤r≤1
The larger |r|is, the stronger is the linear relationship. r ≈0
indicates that there is no linear relationship between X and Y. r = 1 or -
1 implies that a perfect linear pattern exists between two variables. r >0
tells the positive relationship and r <0 means the negative one.
•Sum of Squares: SSX=P(x−x)2,SS
Y=P(y−y)2,
•Sum of Cross Product: SCPXY =P(x−x)(y−y)
•Standard Deviation of X: SX=qSSX
n−1
•Standard Deviation of Y: SY=qSSY
n−1
•Covariance, cov(X,Y): A measure of the joint variation of the two vari-
ables.
cov(X,Y) = 1
n−1P(x−x)(y−y)= 1
n−1SCPXY.
1
