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    Regressions and scattergrams

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    3.7 Based on the data for the United States for the period 1970 to 1983, the following regression results were obtained:

    GNPt = -787.4723 + 8.0863M1t r2 = 0.9912

    se = ( ) (0.2197)

    t= (-10.10001) ( )

    where GNP is the gross national product (S, in billions) and M1 is the money supply (S, in billions)
    Note: M1 includes currency, demand deposits, travelers checks, and other checkable deposits.

    a. Fill in the blank parentheses.
    b. The monetarist maintain that the money supply has a significant positive impact on GNP. How would you test this hypothesis?
    c. What is the meaning of the negative intercept?
    d. Suppose M1 for 1984 is $552 billion. What is the mean forecast value GNP for that year?

    4.14 Table 7-5 gives data on X [net profits after tax in U.S. manufacturing industries ($, in millions)] and Y [cash dividend paid quarterly in manufacturing industries ($, in millions)] for years 1974 to 1986.

    a. What relationship, if any, do you expect between cash dividend and after tax profits?
    b. Plot the scattergram between Y and X.
    c. Does the scattergram support your expectation in part (a)?
    d. If so, do an OLS regression of Y on X and obtain the usual statistics.
    e. Establish a 99% confidence interval for the true slope and test the hypothesis that the true slope coefficient is zero; that is, there is no relationship between dividend and the after-tax profit.

    Year Y X Year Y X
    ($ in Millions) ($ in Millions)
    1974 19,467 58,747 1981 40,317 101,302
    1975 19,968 49,135 1982 41,259 71,028
    1976 22,763 64,519 1983 41,624 85,834
    1977 26,585 70,366 1984 45,102 107,648
    1978 28,932 81,148 1985 45,517 87,648
    1979 32,491 98,698 1986 46,044 83,121
    1980 36,495 92,579 1987

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    Solution Preview

    Your answers are in the attached Word and Excel files.

    I hope this helps!

    I have now translated all the relevant names into English (I've just noticed I had left a couple untranslated). Please ignore the table called "Analisis de Varianza" (which means "Variance Analysis") in the "Regression" sheet because it's not used in order to answer your questions. I've deleted it in the Excel document I'm attaching now. This Excel sheet was done using the Data Analysis toolpack that comes with Excel, which allows to run OLS regressions. Of course, the regression can be done with your program of choice (such as Minitab) and the results should be exactly the same.

    Regarding which part is question d which is e, ...

    Solution Summary

    Regressions and scattergrams are presented.