Multiple Regression
BPS chapter 28
© 2006 W.H. Freeman and Company
Parallel regression lines
What is always true about two parallel regression lines?
a)
b)
c)
d)
The slopes are approximately the same.
The intercepts are approximately the same.
Both the slopes and the intercepts are approximately the same.
None of the above.
Parallel regression lines (answer)
What is true about two parallel regression lines?
a)
b)
c)
d)
The slopes are approximately the same.
The intercepts are approximately the same.
Both the slopes and the intercepts are approximately the same.
None of the above.
Indicator variable
When do we use an indicator variable in a regression equation?
a)
b)
When we have a quantitative variable with two possible answers, 0
and 1.
When we have a categorical variable with two possible answers,
one we assign the code “0” and the other we assign the code “1”.
Indicator variable (answer)
When do we use an indicator variable in a regression equation?
a)
b)
When we have a quantitative variable with two possible answers, 0
and 1.
When we have a categorical variable with two possible
answers, one we assign the code “0” and the other we assign
the code “1”.
Regression vocabulary
The formula “observed y – predicted y” is the
a)
b)
c)
d)
e)
Correlation
Regression
R2
Residual
Measure of Normality
Regression vocabulary (answer)
The formula “observed y – predicted y” is the
a)
b)
c)
d)
e)
Correlation
Regression
R2
Residual
Measure of Normality
Parameters
The parameters for multiple regression are:





X and Y.
The ’s.
The  and .
The correlation and standard deviation.
The ’s and .
Parameters (answer)
The parameters for multiple regression are:





X and Y.
The ’s.
The  and .
The correlation and standard deviation.
The ’s and .
ANOVA
If we reject the null hypothesis for the ANOVA F-test, what does that
tell us about our multiple regression model?
a)
b)
c)
d)
e)
All of our  parameters are 0.
All of our  parameters are not 0.
One of our  parameters is 0.
One of our  parameters is not 0.
At least one of our  parameters is not 0.
ANOVA (answer)
If we reject the null hypothesis for the ANOVA F-test, what does that
tell us about our multiple regression model?
a)
b)
c)
d)
e)
All of our  parameters are 0.
All of our  parameters are not 0.
One of our  parameters is 0.
One of our  parameters is not 0.
At least one of our  parameters is not 0.
Significance
How do you know which coefficients are significant?
a)
b)
c)
d)
Perform a t-test for each coefficient, and any with small P-values are
significant.
Perform a t-test for each coefficient, and any with large P-values are
significant.
Perform an F-test for all coefficients, and if the P-value is small, all
coefficients are significant.
Perform an F-test for all coefficients, and if the P-value is large, all
coefficients are significant.
Significance (answer)
How do you know which coefficients are significant?
a)
b)
c)
d)
Perform a t-test for each coefficient, and any with small Pvalues are significant.
Perform a t-test for each coefficient, and any with large P-values are
significant.
Perform an F-test for all coefficients, and if the P-value is small, all
coefficients are significant.
Perform an F-test for all coefficients, and if the P-value is large, all
coefficients are significant.
Interaction
Which of the following is FALSE if you have interaction between two
explanatory variables, x1 and x2?
a)
b)
c)
d)
The individual regression lines for each explanatory variable will be
parallel.
The interaction term can be expressed as x1x2 in the model.
The relationship between the mean response and one explanatory
variable changes when we change the value of the other
explanatory variable.
The interaction term changes the slope of the full model from the
slope of either of the simple (one x-variable) regression models.
Interaction (answer)
Which of the following is FALSE if you have interaction between two
explanatory variables, x1 and x2?
a)
b)
c)
d)
The individual regression lines for each explanatory variable
will be parallel.
The interaction term can be expressed as x1x2 in the model.
The relationship between the mean response and one explanatory
variable changes when we change the value of the other
explanatory variable.
The interaction term changes the slope of the full model from the
slope of either of the simple (one x-variable) regression models.
Multiple regression models
True or false: When considering which model is the best one for your
setting, you should assume you have parallel regression lines (no
interaction) in your model before considering a model with an
interaction term.
a)
b)
True
False
Multiple regression models (answer)
True or false: When considering which model is the best one for your
setting, you should assume you have parallel regression lines (no
interaction) in your model before considering a model with an
interaction term.
a)
b)
True
False
Multiple regression
True or false: The relationship between y and any explanatory variable
can change greatly depending on which other explanatory variables
are present in the model.
a)
b)
True
False
Multiple regression (answer)
True or false: The relationship between y and any explanatory variable
can change greatly depending on which other explanatory variables
are present in the model.
a)
b)
True
False
Residual plots
What does it mean if you see a quadratic pattern in your residual plot?
a)
b)
c)
d)
All the regression assumptions were met.
There are many outliers.
The Normality assumption was not met.
An x2 term may need to be added to the model.
Residual plots (answer)
What does it mean if you see a quadratic pattern in your residual plot?
a)
b)
c)
d)
All the regression assumptions were met.
There are many outliers.
The Normality assumption was not met.
An x2 term may need to be added to the model.
Multiple regression models
Which of the following is NOT an important indication of a good model?
a)
b)
c)
d)
e)
The ANOVA F-test rejected the null hypothesis.
R2 is close to 100%.
The 0 coefficient is significant.
The i coefficients in the model (not counting 0) are significant.
The residual plot shows a random scattering of points.
Multiple regression models (answer)
Which of the following is NOT an important indication of a good model?
a)
b)
c)
d)
e)
The ANOVA F-test rejected the null hypothesis.
R2 is close to 100%.
The 0 coefficient is significant.
The i coefficients in the model (not counting 0) are significant.
The residual plot shows a random scattering of points.