Statistical Modeling and Regression Analysis of Economic Variables

This document presents a detailed solution to a statistics homework assignment focused on regression analysis. The assignment involves analyzing economic data using multiple regression models, with independent variables including the Federal Funds Rate (FFUNDS), Money Supply (MZM), Consumer Price Index (CPI), and Disposable Income (YD). The solution tests for the significance of explanatory variables, assesses the overall utility of the model using ANOVA, and determines the best model by considering various transformations of the explanatory variables (square, reciprocal, and natural logs). Furthermore, the solution incorporates a dummy variable for the period of democratic presidents and performs a Chow test to check for structural changes in the relationship between money supply and other variables after the first quarter of 2008. The analysis provides insights into the statistical significance of different variables and models, aiding in understanding the relationships within the economic data.

STATISTICS
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Grizli777

Independent variables Dependent variable
FFUNDS = Federal Funds Rate,
CPI = Consumer Price Index,
YD= Disposable Income,
TREND = Trend or Observation Number
MZM = Money Supply
 Multiple regression model
Test for significance for explanatory variable
Assuming significance level (alpha) = 0.05
The slope coefficient would be said statistically significant when the corresponding p value is
lower than the level of significance.
Hence, it can be said the slope of disposable income would be significant and the other slope
coefficients are insignificant.
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Test to check the overall utility of model
ANOVA Table
It can be seen that the significance F (p value) comes out to be zero which is lower than the
significance level. Thus, it can be concluded that the regression model is statistically
significant for the analysis.
Best Model Determination
 Regression model (Full model considering the square of explanatory variables)
 Regression model (Full model considering the reciprocal of explanatory variables)
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 Regression model (Full model considering the natural logs of explanatory variables)
The best model seems to be the one in which the square of explanatory variables have been
taken into consideration. This is the best model as the value of R2 and adjusted R2 is the
highest for this particular model as compared to other models.
Significance of Democratic Dummy Variable
 Regression model (Full model considering the dummy variable for democratic president
period)
Variable democratic president = 1 for the below mentioned period and 0 for the rest of the
years
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The p value associated with the slope of the dummy variable for democratic year is lower
than 0.05 (assumed significance level). As a result, it can be concluded that the given dummy
variable is statistically significant.
Chow Test
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The significance F comes out to be 0.047 which is lesser than 0.05 and hence, it can be said
that the claim is correct that the relationship between money supply and all other variables
have changed after first quarter of 2008.
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