Page 138 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

relationship exists when changes in one variable tend to be
accompanied by consistent and predictable changes in the other
variable.
A regression line summarizes the best relationship between an
independent variable and a dependent variable. The regression line
is used to predict values of y, given a value of x. The stronger the
correlation between two variables, the more accurate the
predictions is. The values of X can be entered into the regression
equation and the predicted Y values are provided.

Least-Squares Regression Equation
ˆ
Y  bX  a

1. b is the slope of the regression line. One unit change in X is
equal to “b” unit changes in Y.

 S 
b   r  Y 

 S X 
2. a is the intercept. The value of Y when X = 0

a  Y  b X

3. When the value of the predicted y does not equal the value
of the observed y, the difference is called a residual (error).

The Theory and Applications of Statistical Inferences 122