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# Regressions and scattergrams

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(See attached file for full problem description)

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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.

Table 7-5 CASH DIVIDENT (y) AND AFTER-TAX PROFITS (X) IN U.S.
MANUFACTURING INDUSTRIES, 1974-1986.
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

https://brainmass.com/economics/econometric-models/regressions-and-scattergrams-72379

#### Solution Preview

Hello!

I hope this helps!

UPDATE FROM OTA:
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.

\$2.19

## Notes on Scattergrams, hypothesis, confidence interval

(See attached file for full problem description)

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1.7 Based on the data for the years 1962 to 1977 for the United States, Dale Bails and Larry Peppers17 obtained the following demand function for automobiles:

Yt = 5807 + 3.24Xt r2 = 0.22

Se = (1.634)

Where Y = retail sales of passenger cars (thousands) and X = the real disposable income (billions of 1972 dollars).
Note: The se for b1 is not given.
a. Establish a 95% confidence interval for B2.
b. Test the hypothesis that this interval includes B2 = 0. If not, would you accept this null hypothesis?
c. Compute the t value under H0: B2 = 0. Is it statistically significant at the 5 percent level? Which t test do you use, one tailed or two tailed, and why?

2.7 The characteristic line of modern investment analysis involves running the following regression:

rt = B1 + B2r mt + ut

where r = the rate of return on a stock or security
rm = the rate of return on the market portfolio represented by a broad market index such as S&P 500, and
t = tine

In investment analysis, B2 is known as the beta coefficient of the security and is used as a measure of market risk, that is, how developments in the market affect the forunes of a given company.

Based on 240 monthly rates of return for the period 1956 to 1976, Fogler and Ganapathy obtained the following results for IBM stock. The market index used by the authors is the market portfolio index developed at the University of Chicago.

rt = 0.7264 = 1.0598r mt

se = (0.3001) (0.0728) r2 = 0.4710

a. Interpret the estimated intercept and slope.
b. How would you interpret r2?
c. A security whose beta coefficient is greater than 1 is called a volatile or aggressive security. Set up the appropriate null and alternative hypothesis and test them using the t test. Note: Use a =5

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