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Which observations, when excluded, cause a significant change to model coefficients?
A) Observations 1, 10, and 11.
B) Observations 10 and 19.
C) Observation 19.
Toni Williams, CFA, has determined that commercial electric generator sales in the Midwest
U.S. for Self-Start Company is a function of several factors in each area: the cost of heating
oil, the temperature, snowfall, and housing starts. Using data for the most currently
available year, she runs a cross-sectional regression where she regresses the deviation of
sales from the historical average in each area on the deviation of each explanatory variable
from the historical average of that variable for that location. She feels this is the most
appropriate method since each geographic area will have different average values for the
inputs, and the model can explain how current conditions explain how generator sales are
higher or lower from the historical average in each area. In summary, she regresses current
sales for each area minus its respective historical average on the following variables for each
area.
The difference between the retail price of heating oil and its historical average.
The mean number of degrees the temperature is below normal in Chicago.
The amount of snowfall above the average.
The percentage of housing starts above the average.
Williams used a sample of 26 observations obtained from 26 metropolitan areas in the
Midwest U.S. The results are in the tables below. The dependent variable is in sales of
generators in millions of dollars.
Coefficient Estimates Table
Variable
Estimated Coefficient
Standard Error of the
Coefficient
Intercept
5.00
1.850
$ Heating Oil
2.00
0.827
Low Temperature
3.00
1.200
Snowfall
10.00
4.833
Housing Starts
5.00
2.333
Analysis of Variance Table (ANOVA)
Source
Degrees of Freedom
Sum of Squares
Mean Square
Regression
4
335.20
83.80
Error
21
606.40
28.88
Total
25
941.60
Table of the F-Distribution
Critical values for right-hand tail area equal to 0.05
Numerator: df1 and Denominator: df2
df1
df2
1
2
4
10
20
1
161.45
199.50
224.58
241.88
248.01
2
18.513
19.000
19.247
19.396
19.446
4
7.7086
6.9443
6.3882
5.9644
5.8025
10
4.9646
4.1028
3.4780
2.9782
2.7740
20
4.3512
3.4928
2.8661
2.3479
2.1242
One of her goals is to forecast the sales of the Chicago metropolitan area next year. For that
area and for the upcoming year, Williams obtains the following projections: heating oil prices
will be $0.10 above average, the temperature in Chicago will be 5 degrees below normal,
snowfall will be 3 inches above average, and housing starts will be 3% below average.
In addition to making forecasts and testing the significance of the estimated coefficients, she
plans to perform diagnostic tests to verify the validity of the model's results.