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A Look at the Methods Used in Regression Analysis

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The intention of this research project was to build an empirically based model that could be used to prepare a forecast of future consumption. The first step that must be taken is to study the effects of income and interest rates on the consumption of non-durable goods for the years 1990 to 1994. To forecast future consumption, Microsoft EXCEL was used to produce both simple and multiple regressions from the data period 1991 through 1993 data. In the simple regression model, income was used as the independent variable. Interest rates along with income provided the independent variables in the multiple regression analysis. The best resulting regression equations were determined and used to forecast consumption for the year 1994.

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Regression analysis is the statistical technique most frequently used in the field of economics to process empirical evidence and to test the explanatory power of theoretical models. In order to forecast future consumption and compare the results to theoretical models, simple and multiple regressions were run. All data needed to run the regression was taken from the Federal Reserve Bank of St. Louis data bank (FREDDATA). Monthly data in chained 1992 dollars is used for both consumption expenditure and disposable income. The monthly data was lagged five to twelve months and analyzed to find the best equation. The lag was needed so that it could not be argued that changes in income cause changes in spending, or that changes in spending cause changes in income. The seasonally adjusted annual rate (SAAR) also played a role in the data transformation process so that no other outside factors, such as the seasons, could be responsible for the regression results.

After the regression analysis was finished, the next step was to determine which; of the economic theories best explained the results of the data analysis. To help explain these theories and results, Millers Economics Today, Picconi, Romano, and Olsons Business Statistics: Elements and Applications, Wyricks The Economists Handbook: A Research and Writing Guide, and Neufelds Learning Business Statistics with Microsoft Excel 97, were used as resources. In the next few pages, information from these texts will be utilized to explain economic theories, regressions, and results dealing with the relationship between disposable income and interest rates and consumption of non-durable goods.

In this analysis, I will show that the regression data partially agrees with both Keyness theory of consumption as well as the classical model of consumption. In order to predict future consumption expenditures, it was necessary to rely on both theories of consumption since income and interest rates were the two variables concerned. The following paragraphs will describe these two economic theories.

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To prepare this analysis it was essential to rely on Keynes theories about consumption. Keynes consumption function argued that saving and consumption decisions depend primarily on an individuals current real disposable income (Miller, 272). This differs from the Classical Model, in which interest rates determine consumption. According to Keynes, the interest rate is not the most important determinant of an individuals saving and consumption decisions. Keynes proposition stated that how much a person earns determines how much they will consume.

At the middle of Keynes theory was the idea that as real disposable income increases; planned consumption will also increase, but not as significantly. Under the assumption of a fixed price model, Keynes stated that a change in consumption would have the same sign as a change in income. In Lehmans terms the more people make, the more they will spend. When consumers predict or experience an increase in real income, they will be more likely to spend that income rather than save it for the future. In contrast, if the consumer were to anticipate a decrease in real income, they will tend to save their income rather than consume it.

In the hypothetical graph and equation shown below, consumption is illustrated as a function of real income. It is simple to see that as the income levels increase, consumption progressively increases in steps. This complements Keynes theory that the change in income and the change in consumption will have the same sign.

Next we must inspect the theory that deals with interest rates and whether or not they play a role in consumption. Macroeconcomists of the 1940s, including James D. Duesendary who published Income, Saving, and the Theory of Consume Behaving, following the lead of Sir John R. Hicks, started including interest rates as a determinant of consumption. Keynes model is the only theory among economist that does not include interest rates as a determinant factor in consumption. The classical model, and most others, follow the belief that when interest rates are high, people will save more, and therefore consume less. When interest rates are high consumers tend to invest their money in a bank. During this period of high interest it is more expensive for them to borrow money and they will decrease consumption.

This analysis was prepared using nominal rates of interest rather than real rates of interest because of their unpredictability during times of high inflation. Real rates of interest are nominal rates of interest minus the anticipated rate of inflation. Nominal interest rates and their effects on consumption of non durable goods will studied in our hypothetical model, since inflation does not factor in the analysis.

The graph prepared below shows what would be the consequences if the impact of interest rates would cause a five hundred dollar decrease in consumption. The result is that the y-intercept of the consumption curve shifts downward. The equation also shown below was used to derive the graph, states that consumption is equal to savings plus income plus the effect of interest rates.

After computing the simple regression equation, the best lag in months needed to be determined. For consumption of non-durable goods, disposable personal income lagged seven months produced the highest R Squared, 0.888. Neufeld states that R Square, or the coefficient of determination, explains, how well the regression line fits the particular sample on which it has been estimated (Neufeld, 350). When analyzed R Square must be between zero and one. Since the value for YPDI-7 was 0.888, this means the over 88% of the variation in the consumption of non-durable goods is explained by the variation in disposable personal income.

Next we must observe the p-value, or probability value. The p-value represents the probability of finding sample results as abnormal as the one that was actually observed (Picconi, Olson, and Romano, 345). Since the p-value for YPDI-7 lag was exceptionally small, the equation is statistically significant. The smaller the p-value indicates a greater significance. The p-values shown in the chart below indicate a high level of significance.

The best single summary number available from the simple regression analysis is the mean absolute percentage error or MAPE. For the simple regression, the MAPE for the fit or historical data was 0.57. When we forecasted our data for the next year the MAPE was 1.64, more than the fit MAPE, which was expected. There really are no rules about good or poor MAPEs, clearly 0.60 is a small number. This equation produced a better fit than forecast MAPE. After we have analyzed the multiple regression and explained, the MAPEs from both analyses can be compared and discussed.

The results after our analysis agree with the Keynesian theory that changes in income are related to changes in consumption, and that these changes will produce the same sign. In this case, the sign produced was positive. The table shown below clearly shows which lag produced the highest R Square, what the coefficients were for each lag, and also each p-value. The p-values were very small that when rounded to three decimal points, they showed zero, indicating a very high level of significance. Also shown below is the equation derived from the YPDI-7 simple regression.

SIMPLE REGRESSION RESULTS

Next we must do an in depth analysis of the multiple regression which is a bit more intricate. In our simple regression we used the R Square as the only determinant to find the best lag, the multiple regression will use various determinants. If the negative coefficient is present, then the p-values had to be examined for significance. Since the coefficient is known, the p-value had to be divided in half to make the test one-tail rather than a two-tail test (Picconi, Olson, and Romano, 345). The p-value was the smallest for iGS3-12, so this regression was used for the equation.

The adjusted R Square from the output was 0.8859. Over 88% of the variation in consumption is explained by the two variables, income and interest rates. In our analysis the multiple regression produced a higher R Square than the simple regression. This means that more of the variation in consumption was explained by the variation in interest rates rather than in income.

After the regressions were completed for the multiple regression the MAPEs needed to be figured. For the fit data, the MAPE was 0.44, and for the forecasted data, the MAPE was 1.65. The MAPE for the multiple regression was lower than the simple regression, but for the forecasted data the simple regression was .01 lower. The multiple regression produced a better fit MAPE but a very similar forecasted MAPE.

Since our multiple regression when computed produced a negative coefficient with a low p-value, there was a need for further analysis. These results follow the classical theory that interest rates are related to consumption expenditures. The table shown below identifies the lags and their corresponding R Squares for the multiple regression. Coefficients and p-values are also shown, along with the interest rate coefficients and p-values. Highlighted below is the multiple regression equation that was used to predict consumption expenditures in 1994.

As stated before the Keynesian economic model suggested that the consumer income level and consumption expenditures were closely related. In turn the classical model proposed that interest rates played the key role in the consumers amount of consumption. While we have analyzed, predicted, and forecast it is now evident that both theories have some accuracy. It appears when interest rates enter into the equation our results were more accurate then without them. So with the analysis of the regression output we are influenced by the classical view rather than the Keynesian view.

The results of the simple regression follow Keynesian theory very closely. Income in this analysis does play a key role in consumption. By creation a regression plot we can see how closely the predicted consumption values are to the actual values. In the regression plot created below, it is clear that the fit data lies closely around the line, but the forecasted data is overestimated.

When interest rates were added to our equation, the results were consistent with the classical theory that interest rates were the main determinant of consumption. We can see from our multiple regression analysis our fit data for consumption of non-durable goods fit even closer than the simple regression. The simple regression and multiple regressions forecasted data values are very closely related.

Forecasting future consumption for 1994 was the main point of this paper. According to the MAPEs, the results from the regressions are closely related to the classical theory rather than Keynes theory. In conclusion, this analysis has shown that both income and interest rates play a role in prediction consumption. However interest rates have provided us with a better fit for our actual values, but the forecasting equation was actually better fit for the simple regression. The forecasted value for the MAPEs was very close to each other in both regressions. More research and other factors need to be considered to complete the study.

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A Look at the Methods Used In Regression Analysis. (2019, March 12). GradesFixer. Retrieved February 27, 2021, from https://gradesfixer.com/free-essay-examples/a-look-at-the-methods-used-in-regression-analysis/
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A Look at the Methods Used In Regression Analysis. [online]. Available at: <https://gradesfixer.com/free-essay-examples/a-look-at-the-methods-used-in-regression-analysis/> [Accessed 27 Feb. 2021].
A Look at the Methods Used In Regression Analysis [Internet]. GradesFixer. 2019 Mar 12 [cited 2021 Feb 27]. Available from: https://gradesfixer.com/free-essay-examples/a-look-at-the-methods-used-in-regression-analysis/
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