Module 5

Question 1

We use ___________ to investigate the relationship between a dependent variable and multiple
independent variables.

Answer 1

multiple regression

Question 2

The structure of the multiple regression equation is…

Answer 2

y^=a+b1x1+b2x2+…+bkxk.

Question 3

The true relationship between multiple variables is described by y=α+β1x1+β2x2+…+βkxk+ε, where ε is the ________.

Answer 3

error term

Question 4

_________ in multiple regression characterize relationships that are net with respect to the independent variables included in the model but gross with respect to all omitted independent variables.

Answer 4

Coefficients

Question 5

Forecasting with a multiple regression equation is similar to forecasting with a single variable linear model. However, instead of entering only one value for a single independent variable, we input a value for ______ of the independent variables.

Answer 5

each

Question 6

As with single variable linear regression, it is important to evaluate several metrics to determine whether a multiple variable linear regression model is a ______ for our data.

Answer 6

good fit

Question 7

For multiple regression we rely less on scatter plots and more on __________ and _________ because visualizing three or more variables can be difficult.

Answer 7

numerical values; residual plots

Question 8

Because R2 never ________ when independent variables are added to a regression, it is important to multiply it by
an ____________ when assessing and comparing the fit of a multiple regression model.

Answer 8

decreases; adjustment factor

Question 9

This adjustment factor compensates for the ________ in R2 that results solely from increasing the number of independent variables.

Answer 9

increase

Question 10

It is particularly important to look at ________, rather than R2, when comparing regression models with different numbers of independent variables.

Answer 10

Adjusted R2

Question 11

In addition to analyzing Adjusted R2, we must test whether the relationship between the independent and dependent variables is ______ and _______. We do this by analyzing the regression’s residual plots and the _______
associated with each independent variable’s coefficient.

Answer 11

linear; significant; p-values

Question 12

For multiple regression models, because it is difficult to view the data in a simple scatter plot, ________ are an
indispensable tool for detecting whether the linear model is a good fit.

Answer 12

residual plots

Question 13

There is a residual plot for each _______ variable included in the regression model.

Answer 13

independent

Question 14

We can graph a residual plot for each independent variable to help detect patterns such as __________ and __________.

Answer 14

heteroskedasticity; nonlinearity

Question 15

As with single variable regression models, if the underlying multiple relationship is linear, each of the residuals
follows a normal distribution with a mean of _____ and _____ variance.

Answer 15

zero; fixed

Question 16

We should also analyze the _______ of the independent variables to determine whether there is a significant
relationship between the variables in the model.

Answer 16

p-values

Question 17

If the p-value of each of the independent variables is less than _____, we conclude that there is sufficient evidence to say that we are 95% confident that there is a significant linear relationship between the independent and dependent variables.

Answer 17

0.05

Question 18

Multiple regression requires us to be aware of the possibility of __________ among the independent variables.

Answer 18

multicollinearity

Question 19

Multicollinearity occurs when there is a ______ linear relationship among two or more of the independent
variables.

Answer 19

strong

Question 20

Indications of multicollinearity include seeing an independent variable’s p-value ________ when one or more other independent variables are added to a regression model.

Answer 20

increase

Question 21

We may be able to _______ multicollinearity by either increasing the ________ size or removing one (or more) of
the collinear variables.

Answer 21

reduce; sample

Question 22

Multiple regression models allow us to include multiple __________ for categorical data—day of week,
for example.

Answer 22

dummy variables

Question 23

A dummy variable is equal to ___ when the variable of interest fits a certain criterion. For example, a dummy
variable for “Saturday” would equal ___ for observations relating to Saturdays and ___ for observations related
to all other days.

Answer 23

1; 1; 0

Question 24

The number of dummy variables we include must always be ___ fewer than the number of options in a category.

Answer 24

1

Question 25

_________ are used to capture the ongoing effects of a given variable.

Answer 25

Lagged values

Question 26

The lag period is based on managerial _____ and data _______.

Answer 26

insight; availability

Question 27

If the lagged variable does not _______ the model’s explanatory power, the addition of the variable
decreases Adjusted R2.

Answer 27

increase

Question 28

How do you create a regression output table in excel?

Answer 28

Using the Data Analysis tool

Question 29

How do you create a regression model using dummy variables?

Answer 29

=IF(logical_test,[value_if_true],[value_if_false])

→ Returns value_if_true if the specified condition is met, and returns value_if_false if the condition is not met.