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

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    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?
    a. adjusted r2
    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
    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

    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
    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 = β0 + β1 X1 + β2 X2 + β3 X1X2 + β4 X12 + β5 X12X2 + ε
    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
    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
    a. H0 : β2 = β3 = β5 = 0
    b. H0 : β3 = β5 = 0
    c. H0 : β4 = β5 = 0
    d. H0 : β2 = 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 β-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
    a. quadratic trend analysis.
    b. the MAD.
    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.
    b. quadratic 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.
    d. compute the MAD statistic.

    20. Which of the following statements about moving averages is not
    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
    a. 36
    b. 40.5
    c. 54
    d. 72

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    Solution Summary

    Twenty regression problems are solved.