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    Multiple Regression Models and Simple Linear Regression Models (21 Problems) : Least Squares, Durbin-Watson, Correlation Coefficient, Standard Error and p-Values

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    1. The y-intercept (b0) represents the
    a. predicted value of Y when X = 0.
    b. change in estimated average Y per unit change in X.
    c. predicted value of Y.
    d. variation around the sample regression line.

    2. The least squares method minimizes which of the following?
    a. SSR
    b. SSE
    c. SST
    d. All of the above

    TABLE 1
    A candy bar manufacturer is interested in trying to estimate how sales are
    influenced by the price of their product. To do this, the company randomly
    chooses 6 small cities and offers the candy bar at different prices. Using
    candy bar sales as the dependent variable, the company will conduct a
    simple linear regression on the data below:

    City Price ($) Sales
    River Falls 1.30 100
    Hudson 1.60 90
    Ellsworth 1.80 90
    Prescott 2.00 40
    Rock Elm 2.40 38
    Stillwater 2.90 32

    Referring to Table 1, what is the estimated slope parameter for the
    candy bar price and sales data?
    a. 161.386
    b. 0.784
    c. -3.810
    d. -48.193

    4. Referring to Table 1, what is the percentage of the total variation in
    candy bar sales explained by the regression model?
    a. 100%
    b. 88.54%
    c. 78.39%
    d. 48.19%

    5. Referring to Table 1, what is the standard error of the estimate, SYX,
    for the data?
    a. 0.784
    b. 0.885
    c. 12.650
    d. 16.299

    6. Referring to Table 1, if the price of the candy bar is set at $2, the
    predicted sales will be
    a. 30
    b. 65
    c. 90
    d. 100

    7. If the Durbin-Watson statistic has a value close to 0, which
    assumption is violated?
    a. Normality of the errors.
    b. Independence of errors.
    c. Homoscedasticity.
    d. None of the above.

    8. If the Durbin-Watson statistic has a value close to 4, which
    assumption is violated?
    a. Normality of the errors.
    b. Independence of errors.
    c. Homoscedasticity.
    d. None of the above.

    9. If the correlation coefficient (r) = 1.00, then
    a. the y-intercept (b0) must equal 0.
    b. the explained variation equals the unexplained variation.
    c. there is no unexplained variation.
    d. there is no explained variation.

    10. In a simple linear regression problem, r and b1
    a. may have opposite signs.
    b. must have the same sign.
    c. must have opposite signs.
    d. are equal.

    11. The strength of the linear relationship between two numerical
    variables may be measured by the
    a. scatter diagram.
    b. y-intercept.
    c. slope.
    d. coefficient of correlation.

    12. The width of the prediction interval estimate for the predicted value
    of Y is dependent on
    a. the standard error of the estimate.
    b. the value of X for which the prediction is being made.
    c. the sample size.
    d. All of the above.

    TABLE 2
    The following Excel tables are obtained when "Score received on an
    exam (measured in percentage points)" (Y) is regressed on
    "percentage attendance" (X) for 22 students in a Statistics for
    Business and Economics course.

    Regression Statistics
    Multiple R 0.142620229
    R Square 0.02034053
    Adjusted R Square -0.028642444
    Standard Error 20.25979924
    Observations 22

    Coefficients Standard Error t Stat p-value
    Intercept 39.39027309 37.24347659 1.057642216 0.302826622
    Attendance 0.340583573 0.52852452 0.644404489 0.526635689

    13. Referring to Table 2, which of the following statements is true?
    a. -2.86% of the total variability in score received can be
    explained by percentage attendance.
    b. -2.86% of the total variability in percentage attendance can
    be explained by score received.
    c. 2% of the total variability in score received can be explained
    by percentage attendance.
    d. 2% of the total variability in percentage attendance can be
    explained by score received.

    14. In a multiple regression problem involving two independent
    variables, if b1 is computed to be +2.0, it means that
    a. the relationship between X1 and Y is significant.
    b. the estimated average of Y increases by 2 units for each
    increase of 1 unit of X1, holding X2 constant.
    c. the estimated average of Y increases by 2 units for each
    increase of 1 unit of X1, without regard to X2.
    d. the estimated average of Y is 2 when X1 equals zero.

    15. In a multiple regression model, which of the following is correct
    regarding the value of the adjusted r2?
    a. It can be negative.
    b. It has to be positive.
    c. It has to be larger than the coefficient of multiple
    determination.
    d. It can be larger than 1.

    16. A manager of a product sales group believes the number of sales
    made by an employee (Y) depends on how many years that employee
    has been with the company (X1) and how he/she scored on a business
    aptitude test (X2). A random sample of 8 employees provides the
    following:

    TABLE 3
    Employee Y X1 X2
    1 100 10 7
    2 90 3 10
    3 80 8 9
    4 70 5 4
    5 60 5 8
    6 50 7 5
    7 40 1 4
    8 30 1 1
    Referring to Table 3, for these data, what is the value for the
    regression constant, b0?
    a. 0.998
    b. 3.103
    c. 4.698
    d. 21.293

    17. Referring to Table 3, if an employee who had been with the company
    5 years scored a 9 on the aptitude test, what would his estimated
    expected sales be?
    a. 79.09
    b. 60.88
    c. 55.62
    d. 17.98

    TABLE 4
    An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross
    domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.

    SUMMARY OUTPUT

    Regression Statistics
    Multiple R 0.991
    R Square 0.982
    Adjusted R Square 0.976
    Standard Error 0.299
    Observations 10

    ANOVA
    Df SS MS F Signif F
    Regression 2 33.4163 16.7082 186.325 0.0001
    Residual 7 0.6277 0.0897
    Total 9 34.0440

    Coeff StdError t Stat P-value
    Intercept -0.0861 0.5674 -0.152 0.8837
    GDP 0.7654 0.0574 13.340 0.0001
    Price -0.0006 0.0028 -0.219 0.8330
    18. Referring to Table 4, when the economist used a simple linear
    regression model with consumption as the dependent variable and
    GDP as the independent variable, he obtained an r2 value of 0.971.
    What additional percentage of the total variation of consumption
    has been explained by including aggregate prices in the multiple
    regression?
    a. 98.2
    b. 11.1
    c. 2.8
    d. 1.1

    19. Referring to Table 4, what is the predicted consumption level for an
    economy with GDP equal to $4 billion and an aggregate price index
    of 150?
    a. $1.39 billion
    b. $2.89 billion
    c. $4.75 billion
    d. $9.45 billion

    20. Referring to Table 4, to test for the significance of the coefficient on
    aggregate price index, the value of the relevant t-statistic is
    a. 2.365
    b. 0.143
    c. -0.219
    d. -1.960

    21. Referring to Table 4, to test whether gross domestic product has a
    positive impact on consumption, the p-value is
    a. 0.00005
    b. 0.0001
    c. 0.9999
    d. 0.99995

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    https://brainmass.com/math/interpolation-extrapolation-and-regression/43946

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    Solution Summary

    Least Squares, Durbin-Watson, Correlation Coefficient, Standard Error and p-Values are investigated.

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