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20.1
Forrest Tucker, the head statistician for the National Parks Service, believes that
park usage as measured by number of visitors (Y) is a function of the number
of people who live within 200 miles of the park (X), the number of camping
hookups available (X2), and the mean annual temperature at the park (X3). For
a sample of 200 parks under Forrest's supervision, the following regression is
calculated:
8 147 + .0212X1 + 15.4X2 + 186X3
$6,0157 = 12.4 sb = 10.4 R2 = .50 Adj. R2 = .43
For this regression, what can you tell Forrest? Write a one-page memo with your
assessment.
20.2
If Janice Position-Classification, personnel officer for the Bureau of Forms, can
forecast agency separations 6 months from now, she can plan recruitment efforts
to replace these people. Janice believes that separations 6 months from now are
determined by the number of agency people passed over for promotion (X1), the
number of agency people 64 years old or older (X2), and the ratio of government
salaries to private sector salaries (X3). Using regression, Janice finds the following:
8 + .35X1 + .54X2 - 271X3
sb,==.0031 sb,==0.136 263 Sylx = 54
R2 = .89 Adj. R2 = .85 N = 214
Write a one-page memo explaining the results, and then forecast the number of
separations if 418 people are passed over for promotion, 327 people are 64 years
old or older, and government salaries equal those in the private sector.
20.5
Lieutenant Colonel Syl Verleaf is placed in charge of base security at all 240 mili-
tary bases in Europe. Verleaf believes that the crime rate is positively correlated to
the size of the base, the percentage of troops without high school degrees, and the
number of women on base. Verleaf's statistician finds the following:
47.3 + .031X1 + 2.4X2 - .065X3
= .0021 Sby =3.0 = .0027 Sylx = 17.1
R==.80 Adj. R2 = .78
where X is the number of troops on the base, X2 is the percentage of troops with-
out high school degrees, X3 is the number of women on the base, and Y is the
number of serious crimes in a month. Interpret all the regression coefficients, R2
and the intercept. What is the most important independent variable? Ramstein
Air Base has 15,000 troops, 42% of its troops have no high school degree, and
there are 3,000 women on base. What is your best estimate of the number of
crimes per month for this base?
21.1
The Director of Economic Development in Potto Gulch, Wisconsin, is inter-
ested in studying the relationship between business activity and spending on
social welfare programs. Specifically, she hypothesizes that as business activ-
ity increases the boost to the local economy (mainly through job creation)
should result in lower spending on programs for the poor. To test this hy-
pothesis, the director gathers annual data for the last 11 years on three vari-
ables. The dependent variable is annual spending on social welfare programs
(in millions of dollars). The director feels that the number of business per-
mits issued each year is a good indicator of economic activity and selects this
as the first independent variable (BPRMT). The second independent variable
is the number of residents in Potto Gulch (POP). The regression output is
displayed below.
Model Summary
Std. Error of
Model
R
R2
Adj. R2
the Estimate
1
.791
.626
.532
800,770.013
Predictors: (Constant), BPRMT, POP.
ANOVA
Model
Sum of Squares
df
Mean Square
F
Significance
Regression
8,568,393,095,762.110
2
4,284,196,547,881.058
6,681
.020
1
Residual
5,129,860,913,328.790
8
641,232,614,166.099
Total
13,698,254,009,090.910 10
Predictors: (Constant), BPRMT, POP.
Dependent variable: EXPENDIT.
Coefficients
Unstandardized
Standardized
Coefficients
Coefficients
Model
B
Std. Error
Beta
t
Significance
(Constant)
3,655,278.783
8,482,054.890
.431
.678
1
POP
109.855
100.721
.293
1.091
.307
BPRMT
-5,049.119
2,339.638
-.581
-2.158
.063
Dependent variable: EXPENDIT.
(a) Interpret the slopes and intercept for this model. What substantive conclu-
sion can the director make about the relationship between business activity
and spending on social welfare programs?
(b) The director is concerned about the drop in the explanatory power of the
model indicated by the adjusted R2 value. What is probably the reason why
the adjusted R2 is lower than R2?
(c) The director has located data on the actual number of Potto Gulch citizens
receiving social welfare assistance each year. If the director includes this new
variable in the model, which of the current independent variables should be
removed from the model? Explain.
21.2
The director of the Northern Tennessee Association of Local Governments is
conducting a study on differences in average property taxes (in thousands of
dollars) that residents in 15 local communities pay on their homes. The direc-
tor believes that variations in property taxes are a function of two variables: the
number of government employees on staff in each city (EMPLOYEES) and city
size, measured in square miles (SIZE). The director uses SPSS to generate the fol-
lowing regression, where the average property tax per residence is the dependent
variable.
Model Summary
Std. Error of
Model
R
R2
Adj. R2
the Estimate
1
.983
.967
.961
112.85532
Predictors: (Constant), SIZE, EXPLOYEES
ANOVA
Model
Sum of Squares
df
Mean Square
F
Significance
Regression
4,421,115.713
2
2,210,557.857
173.563
.000a
1
Residual
152,835.887
12
12,736.324
Total
4,573,951.600
14
Predictors: (Constant), SIZE EMPLOYEES
beDendent variable: PTAX.
Coefficients
Unstandardized
Standardized
Coefficients
Coefficients
Model
B
Std. Error
Beta
t
Significance
(Constant)
938.736
336.866
2.787
.016
1
Employees
8.225
2.631
.564
3.126
.009
Size
47.532
19.794
- -.430
2.380
.035
Dependent variable: PTAX.
(a) Interpret the intercept, slopes, and R2 values.
(b) Interpret the standardized coefficients. Explain how the standardized
coefficients differ in magnitude from the unstandardized coefficients.

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