Chapter 14
Introduction to Multiple Regression
Sections 1, 2, 3, 4, 6
14.1: Developing the Multiple
Regression Model
• Often, a better-fitting model of the
dependent variable results from using
multiple independent variables.
• Multiple independent variables means
multiple regression.
• The “omni-power” example models sales
as a function of price and promotion.
Software Output
• Be able to construct the model from
the output.
• The technique is still “least squares”
because we are assuming a linear
relationship between each independent
variable and the dependent variable.
Notes on Mechanics
• We refer to “k” explanatory or
independent variables.
• A slope coefficient is interpreted as the
change in the mean of Y for every change
in X1, taking into account the effect of
other X (sometimes said “holding all
other X constant”).
• In multiple regression, this “slope” called
a “net regression coefficient.”
14.2: r2, adjusted r2, and the overall F
test
• R-squared, R2, the proportion of variation in
Y explained by the set of explanatory
variables in the data set.
• R2 will increase every time a new
independent variable is added to the
regression model, EVEN if the new
independent variable is NOT useful.
• Use adjusted R2 to compare models.
Overall F test
• Is there a significant relationship between
the dependent variable and the set of
explanatory variables?
• H0: β1 = β2 = … = βk = 0.
• H1: at least one of the β s ≠ 0.
• Fcalc = MSR/MSE (formula 14.6)
• Table 14.2 defines the test constituents. Use
p.
14.3: Residual Analysis for the
Multiple Regression Model
• Page 580 lists the useful plots. Note
that they are the same plots used in
Chapter 13.
• What are the assumptions?
14.4: Inferences Concerning the
Population Regression Coefficients
• The hypothesis test for a single slope is the
same “t test” used in Chapter 13.
• H0: βi = 0 and H1: βi ≠ 0.
• 1 tailed tests are possible.
• Recommend using the observed
significance, i.e. the “p-value.”
• Important note on page 583.
14.6: Using Dummy Variables and
Interaction Terms in Regression Models
• Dummy: Use categorical independent
variables.
• Interaction: Use products of independent
variables.