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Stochastic Regression Functions

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What are the similarities and/or differences between a stochastic population regression function (PRF) and a stochastic sample regression function (SRF)?

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Hello,

First I would to clarify some important concepts.

- What is a regression?
It is a mathematical expression or a function which shows how 2 or more variables are related. So in a regression we have 1 dependent variable, 1 or more independent variable(s) and an error term. These variables can have a linear or a non-linear relationship depending what theory we want to express with the regression. For example, we know that consumption is a function of income, and other assets. Is this a linear relationship? Yes, because we spend more when we have more money.

The error term indicates that the regression is a stochastic function, i. e. it depends on human behavior. Therefore its estimates will not be 100% accurate. Remember that in econometrics we are dealing with probabilities therefore ...

Solution Summary

The similarities and/or differences between a stochastic population regression function (PRF) and a stochastic sample regression function (SRF).

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See Also This Related BrainMass Solution

Econometrics: Using CPI data, plot a scattergram and analyze

See the attached file forthe formula.

Econometrics

2.12 Table 2-9 gives data on the Consumer Price Index (CPI) for all items (1982-1984=100) and the Standard & Poor's (S&P) index of 500 common stock prices (base of index: 1941-1943=10). Complete letters a through e in the questions that follow the table.

Table 2-9 CONSUMER PRICE INDEX (CPI) AND S&P 500 INDEX (S&P), UNITED STATES, 1978-1989

Year CPI S&P
1978 65.2 96.02
1979 72.6 103.01
1980 82.4 118.78
1981 90.9 128.05
1982 96.5 119.71
1983 99.6 160.41
1984 103.9 160.46
1985 107.6 186.84
1986 109.6 236.34
1987 113.6 286.83
1988 118.3 265.79
1989 124 322.84

a. Plot the data on a scattergram with the S&P index on the vertical axis and CPI on the horizontal axis.

b. What can you say about the relationship between the two indexes? What does economic theory have to say about this relationship?

c. Consider the following regression model:
(S&P)t=B1+B2CPIt+ut
Use the method of least squares to estimate this equation from the preceding data and
interpret your results.

d. Do the results obtained in part c make economic sense?

e. Do you know why the S&P index dropped in 1988?

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