Module 4

Question 1

What are the two primary purposes for using regression?

Answer 1

1. Studying the magnitude and structure of a relationship between two variables.
2. Forecasting a variable based on its relationship with another variable.

Question 2

What is the structure of the single variable linear regression line?

Answer 2

y^=a+bx.

Question 3

What is the expected value of y, the dependent variable, for a given value of x.?

Answer 3

y^

Question 4

What is the independent variable, the variable we are using to help us predict or better understand the dependent
variable.?

Answer 4

x

Question 5

What is the y-intercept, the point at which the regression line intersects the vertical axis. This is the value of y^
when the independent variable, x, is set equal to 0.?

Answer 5

a

Question 6

What is the slope, the average change in the dependent variable y as the independent variable x increases by
one?

Answer 6

b

Question 7

The true relationship between two variables is described by the equation y=α+βx+E, where E is the ______ y–y^.

Answer 7

error term

Question 8

The idealized equation that describes the _________ is y^=α+βx.

Answer 8

true regression line

Question 9

We determine a _________ by entering the desired value of x into the regression equation.

Answer 9

point forecast

Question 10

We must be extremely cautious about using regression to forecast for values outside of the historically observed range of the _________ variable (x-values).

Answer 10

independent

Question 11

Instead of predicting a single point, we can construct a __________, an interval around the point forecast that is likely to contain, for example, the actual selling price of a house of a given size.

Answer 11

prediction interval

Question 12

The ______ of a prediction interval varies based on the standard deviation of the regression (the standard error of the regression), the desired level of confidence, and the location of the x-value of interest in relation to the historical values of the independent variable.

Answer 12

width

Question 13

It is important to evaluate several metrics in order to determine whether a __________________ model is a good fit for a data set, rather than looking at single metrics in isolation.

Answer 13

single variable linear regression

Question 14

_______ measures the percent of total variation in the dependent variable, y, that is explained by the regression line.

Answer 14

R2

Question 15

R2 = Regression Sum of Squares/____________

Answer 15

Total Sum of Squares

Question 16

___≤R2≤____

Answer 16

0; 1

Question 17

For a single variable linear regression, R2 is equal to the _______ of the correlation coefficient.

Answer 17

square

Question 18

In addition to analyzing R2, we must test whether the relationship between the dependent and independent variable is significant and whether the linear model is a good fit for the data. We do this by analyzing the _______ (or confidence interval) associated with the independent variable and the regression’s ________.

Answer 18

p-value; residual plot

Question 19

The _______ of the independent variable is the result of the hypothesis test that tests whether there is a significant _______ relationship; that is, it tests whether the slope of the regression line is zero, H0: β=0 and Ha:β≠0.

Answer 19

p-value; linear

Question 20

If the coefficient’s p-value is less than _____, we reject the null hypothesis and conclude that we have sufficient evidence to be ______ confident that there is a significant linear relationship between the dependent and independent variables.

Answer 20

0.05; 95%

Question 21

Note that the p-value and R2 provide different information. A _________ can be significant (have a low p-value) but not explain a large percentage of the variation (not have a high R2.)

Answer 21

linear relationship

Question 22

A ___________ associated with an independent variable’s coefficient indicates the likely range for that coefficient.

Answer 22

confidence interval

Question 23

If the 95% confidence interval does not contain _____, we can be _____ confident that there is a significant linear relationship between the variables.

Answer 23

zero, 95%

Question 24

__________ can provide important insights into whether a linear model is a good fit.

Answer 24

Residual plots

Question 25

Each observation in a data set has a residual equal to the historically observed value _____ the regression’s predicted value, that is, ______.

Answer 25

minus; E=y-y^

Question 26

Linear regression models assume that the regression’s residuals follow a normal distribution with a mean of _____ and _____ variance.

Answer 26

zero; fixed

Question 27

We can also perform regression analyses using qualitative, or categorical, variables. To do so, we must convert data to ____________.

Answer 27

dummy (0, 1) variables

Question 28

A dummy variable is equal to ____ when the variable of interest fits a certain criterion.

Answer 28

1. For example, a dummy variable for “Female” would equal 1 for all female observations and 0 for male observations.

Question 29

Where do you go to add the best fit line to a scatter plot in excel?

Answer 29

Using the Insert menu

Question 30

What is a convenient function for calculating point forecasts?

Answer 30

=SUMPRODUCT(array1, [array2], [array3],…)

Question 31

Where do you go to create a regression output table in excel?

Answer 31

regression output table using the Data Analysis tool

Question 32

How do you create regression models with dummy variables in excel?

Answer 32

=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.