Question #106
Reading: Reading 1 Multiple Regression
PDF File: Reading 1 Multiple Regression.pdf
Page: 51
Status: Unattempted
Question
Consider the following regression equation: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where Sales is dollar sales in millions, R&D is research and development expenditures in millions, ADV is dollar amount spent on advertising in millions, COMP is the number of competitors in the industry, and CAP is the capital expenditures for the period in millions of dollars. Which of the following is NOT a correct interpretation of this regression information?
Answer Choices:
A. If a company spends $1 million more on capital expenditures (holding everything else constant), Sales are expected to increase by $8.0 million
B. One more competitor will mean $2 million less in Sales (holding everything else constant)
C. If R&D and advertising expenditures are $1 million each, there are 5 competitors, and capital expenditures are $2 million, expected Sales are $8.25 million
Explanation
Predicted sales = $10 + 1.25 + 1 – 10 + 16 = $18.25 million.
(Module 1.1, LOS 1.b)
Autumn Voiku is attempting to forecast sales for Brookfield Farms based on a multiple
regression model. Voiku has constructed the following model:
sales = b0 + (b1 × CPI) + (b2 × IP) + (b3 × GDP) + εt
Where:
sales = $ change in sales (in 000's)
CPI = change in the consumer price index
IP = change in industrial production (millions)
GDP = change in GDP (millions)
All changes in variables are in percentage terms.
Voiku uses monthly data from the previous 180 months of sales data and for the
independent variables. The model estimates (with coefficient standard errors in
parentheses) are:
SALES =
10.2
+ (4.6 × CPI)
+ (5.2 × IP)
+ (11.7 × GDP)
p-value
0.001
0.17
0.11
0.09
The sum of squared errors is 140.3 and the total sum of squares is 368.7.
Voiku calculates the unadjusted R2, the adjusted R2, and the standard error of estimate to
be 0.592, 0.597, and 0.910, respectively.
Voiku is concerned that one or more of the assumptions underlying multiple regression has
been violated in her analysis. In a conversation with Dave Grimbles, CFA, a colleague who is
considered by many in the firm to be a quant specialist, Voiku says, "It is my understanding
that there are five assumptions of a multiple regression model:"
Assumption 1:
There is a linear relationship between the dependent and independent
variables.
Assumption 2:
The independent variables are not random, and there is zero
correlation between any two of the independent variables.
Assumption 3:
The residual term is normally distributed with an expected value of
zero.
Assumption 4:
The residuals are serially correlated.
Assumption 5:
The variance of the residuals is constant.
Grimbles agrees with Miller's assessment of the assumptions of multiple regression.
Voiku tests and fails to reject each of the following four null hypotheses at the 99%
confidence interval:
Hypothesis 1:
The coefficient on GDP is negative.
Hypothesis 2:
The intercept term is equal to –4.
Hypothesis 3:
A 2.6% increase in the CPI will result in an increase in sales of more
than 12.0%.
Hypothesis 4:
A 1% increase in industrial production will result in a 1% decrease in
sales.
Figure 1: Partial F-Table critical values for right-hand tail area equal to 0.05
df1 = 1
df1 = 3
df1 = 5
df2 = 170
3.90
2.66
2.27
df2 = 176
3.89
2.66
2.27
df2 = 180
3.89
2.65
2.26