A First Course in Quality Engineering, 2nd Edition

Continuous Improvement of Quality 487

the chosen α, we reject H

0

: β = 0 and conclude that X and Y have a signicant

linear relationship�

8.3.8.4  Multiple Linear Regression

When there is reason to believe that a dependent variable Y is inuenced by

several independent variables, say, X

1

, X

2

, and Χ

3

, then we use the multiple

linear regression� The regression model will be

 

y x x x

= + + + +α β β β ε

1 1 2 2 3 3

The relationship will be estimated by

 

y a b x b x b x

= + + +

1 1 2 2 3 3

Formulas for a, b

1

, b

2

, and b

3

can be developed the same way as for the

simple regression to minimize the sum of squared deviations� The coefcient

of determination R

2

, ...