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# ANOVA, Regression and Testing of hypothesis problems

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ANOVA, Regression and Testing of hypothesis problems. See attached file for full problem description.

https://brainmass.com/statistics/analysis-of-variance/anova-regression-and-testing-of-hypothesis-problems-91964

#### Solution Summary

The solution gives complete details of computing regression coefficients, test statistics, analysis variance for a set of problems. Interpretation of the results are also given.

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## Regression (20 Problems) : Multiple Regression Model Building, Averages and Exponential Smoothing, Hypothesis Testing and ANOVA

1. A real estate builder wishes to determine how house size (House) is
influenced by family income (Income), family size (Size), and
education of the head of household (School). House size is measured
in hundreds of square feet, income is measured in thousands of
dollars, and education is measured in years. The builder randomly
selected 50 families and ran the multiple regression. The business
literature involving human capital shows that education influences
an individual's annual income. Combined, these may influence
family size. With this in mind, what should the real estate builder
be particularly concerned with when analyzing the multiple
regression model?
a. Randomness of error terms
b. Collinearity
c. Normality of residuals
d. Missing observations

2. A microeconomist wants to determine how corporate sales are
influenced by capital and wage spending by companies. She
proceeds to randomly select 26 large corporations and record
information in millions of dollars. A statistical analyst discovers
that capital spending by corporations has a significant inverse
relationship with wage spending. What should the microeconomist
who developed this multiple regression model be particularly
concerned with?
a. Randomness of error terms
b. Collinearity
c. Normality of residuals
d. Missing observations

3. The Variance Inflationary Factor (VIF) measures the
a. correlation of the X variables with the Y variable.
b. contribution of each X variable with the Y variable after all
other X variables are included in the model.
c. correlation of the X variables with each other.
d. standard deviation of the slope.

4. In multiple regression, the __________ procedure permits variables
to enter and leave the model at different stages of its development.
a. forward selection
b. residual analysis
c. backward elimination
d. stepwise regression

5. Which of the following is not used to find a "best" model?
b. Mallow's Cp
c. odds ratio
d. all of the above

6. The logarithm transformation can be used
a. to overcome violations of the autocorrelation assumption.
b. to test for possible violations of the autocorrelation
assumption.
c. to change a linear independent variable into a nonlinear
independent variable.
d. to change a nonlinear model into a linear model.

7. The Cp statistic is used
a. to determine if there is a problem of collinearity.
b. if the variances of the error terms are all the same in a
regression model.
c. to choose the best model.
d. to determine if there is an irregular component in a time
series.

8. Which of the following is used to determine observations that have
an influential effect on the fitted model?
a. Cook's distance statistic
b. Durbin-Watson statistic
c. variance inflationary factor
d. the Cp statistic

9. An auditor for a county government would like to develop a model to
predict the county taxes based on the age of single-family houses. A
random sample of 19 single-family houses has been selected, with
the results as shown below (and also in the data file TAXES on your
CD-ROM):
____________________________
Taxes Age of House
925 1
870 2
809 4
720 4
694 5
630 8
626 10
562 10
546 12
523 15
480 20
486 22
462 25
441 25
426 30
368 35
350 40
348 50
322 50

Assuming a quadratic relationship between the age of the house and
the county taxes, which of the following is the best prediction of the
average county taxes for a 20-year old house?
a. \$557.30
b. \$481.25
c. \$480.60
d. \$479.15

10. An econometrician is interested in evaluating the relation of
demand for building materials to mortgage rates in Los Angeles and
San Francisco. He believes that the appropriate model is
Y = 10 + 5X1 + 8X2
Where X1 = mortgage rate in %
X2 = 1 if San Francisco, 0 if LA
Y = demand in \$100 per capita
Referring to the information above, holding constant the effect of
city, each additional increase of 1% in the mortgage rate would lead
to an estimated increase of ________ in the mean demand.
a. \$10
b. \$50
c. \$60
d. \$500

11. Referring to the information in #10 above, the fitted model for
predicting demand in Los Angeles is ________.
a. 10 + 5X1
b. 10 + 13X1
c. 15 + 8X2
d. 18 + 5X2

12. Table 3.1
In Hawaii, condemnation proceedings are underway to enable
private citizens to own the property that their homes are built on.
Until recently, only estates were permitted to own land, and
homeowners leased the land from the estate. In order to comply
with the new law, a large Hawaiian estate wants to use regression
analysis to estimate the fair market value of the land. Each of the
following 3 models were fit to data collected for n = 20 properties, 10
of which are located near a cove.
Model 1: Y = &#946;0 + &#946;1 X1 + &#946;2 X2 + &#946;3 X1X2 + &#946;4 X12 + &#946;5 X12X2 + &#949;
where Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square feet
X2 = 1 if property located near cove, 0 if not using the data
collected for the 20 properties, the following partial output
obtained from Microsoft Excel is shown:
SUMMARY OUTPUT_________________________________________
Regression Statistics
Multiple R 0.985
R Square 0.970
Standard Error 9.5
Observations 20
ANOVA
Df SS MS F Signif F
Regression 5 28324 5664 62.2 0.0001
Residual 14 1279 91
Total 19 29063

Coeff StdError t Stat p-value
Intercept -32.1 35.7 -0.90 0.3834
Size 12.2 5.9 2.05 0.0594
Cove -104.3 53.5 -1.95 0.0715
Size*Cove 17.0 8.5 1.99 0.0661
SizeSq -0.3 0.2 -1.28 0.2204
SizeSq*Cove -0.3 0.3 -1.13 0.2749

Referring to Table 3.1, given a quadratic relationship between sale
price (Y) and property size (X1), what null hypothesis would you test
to determine whether the curves differ from cove and non-cove
properties?
a. H0 : &#946;2 = &#946;3 = &#946;5 = 0
b. H0 : &#946;3 = &#946;5 = 0
c. H0 : &#946;4 = &#946;5 = 0
d. H0 : &#946;2 = 0

13. Referring to Table 3.1, is the overall model statistically adequate
at a 0.05 level of significance for predicting sale price (Y)?
a. No, since some of the t-tests for the individual variables are
not significant.
b. No, since the standard deviation of the model is fairly large.
c. Yes, since none of the &#946;-estimates are equal to 0.
d. Yes, since the p-value for the test is smaller than 0.05.

14. The method of moving averages is used
a. to plot a series.
b. to exponentiate a series.
c. to smooth a series.
d. in regression analysis.

15. When using the exponentially weighted moving average for
purposes of forecasting rather than smoothing,
a. the previous smoothed value becomes the forecast.
b. the current smoothed value becomes the forecast.
c. the next smoothed value becomes the forecast.
d. None of the above.

16. In selecting an appropriate forecasting model, the following
approaches are suggested:
a. Perform a residual analysis.
b. Measure the size of the forecasting error.
c. Use the principle of parsimony.
d. All of the above.

17. To assess the adequacy of a forecasting model, one measure that is
often used is
c. exponential smoothing.
d. moving averages.

18. A model that can be used to make predictions about long-term
future values of a time series is
a. linear trend.
c. exponential trend.
d. All of the above.

19. You need to decide whether you should invest in a particular stock.
You would like to invest if the price is likely to rise in the long run.
You have data on the daily average price of this stock over the past
12 months. Your best action is to
a. compute moving averages.
b. perform exponential smoothing.
c. estimate a least square trend model.

20. Which of the following statements about moving averages is not
true?
a. It can be used to smooth a series.
b. It gives equal weight to all values in the computation.
c. It is simpler than the method of exponential smoothing.
d. It gives greater weight to more recent data.

21. The following table contains the number of complaints received in a
department store for the first 6 months of last year.
21. Table 3.2
Month Complaints
January 36
February 45
March 81
April 90
May 108
June 144__
Referring to the Table 3.2 above, if a three-term moving average is
used to smooth this series, what would be the second calculated
term?
a. 36
b. 40.5
c. 54
d. 72

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