Economic Analysis
...ime running regressions on data sets for the purpose of finding trends in data. Fortunately for them, and for us, there are sophisticated software programs that make regression analysis fairly simple. One of these programs is Microsoft’s spreadsheet program, Excel, which is the one that I prefer and the one that is used in this paper. Interpreting the Results: Once a linear regression is performed, there is much data to interpret to find out how well the regression line fits the data and how statistically relevant the study may or may not be. The analysis will produce estimated coefficients of a formula which indicates the degree of relationship between the X and Y and whether it is positive (+) or inverse (-). Generally, the formula is in the form Y = a + bX where a is the Y-intercept and b is the best estimate coefficient of X. But, how relevant is the study to begin with? Is the relationship strong or weak? The t-statistic is a test that will answer the first question. This value is the ratio of the value of the coefficient to its standard error. The larger this number, the more confident you can be that the true coefficient is not zero. If the true value is zero, then there is no relationship between X and Y. As a general rule, if the absolute value of the t-statistic is greater than 2, you can be 95 percent sure that the true value of the coefficient is not zero. P-values are also reported in this analysis and can tell even further how statistically significant the study is. The lower this value, the more confident you can be that the test is relevant. Generally, a P-value of 0.05 or less shows statistical significance. Once you have determined that your study is significantly sound, the answer to the second question, how strong the relationship is, can be sought. R-square, the Coefficient of Determination, tells how well the regression line fits the data points. Basically, R-square is the percentage of the total variation in data that is explained by the regression analysis. The closer to 1 this value is, the better the regression explains the variation, and the better the line fits. The F-statistic also measures the fit of the line. It is similar to R-square in that it measures the total variation explained by the regression, but it makes this relative to the total unexplained variation. The higher the F-statistic, the better the regression line represents the data set. Data Analysis: I collected data for several years of crude oil prices, gasoline prices, US stock market values, US inflation rates, and US automobile sales. Here I will present a chart showing the data for each comparison followed by key statistics. Oil and Gasoline: (InflationData, 2005) The t-statistic between gas and oil is 8.04 and the P-value is near-zero, indicating high statistical relevance. R-square is .71 meaning that 71% of the variation in gasoline prices is explained by the price of oil. Gasoline Prices and the United States Stock Market: (InflationData, 2005 and Yahoo! Finance, 2005) This comparison has a t-statistic of 3.5 which shows some significance. The R-square is .32 so 32% of the variation in the stock market is explained by gasoline prices. This seems opposite to me; I expected to find an inverse relationship. This could indicate that as the stock market performs well, people spend more money, buy more gasoline, and therefore reduce gasoline supply, increasing demand and ultimately increasing the price. Rate of Oil Price Changes and US Inflation Rates: (Department of Labor, 2005 and InflationData, 2005) The t-statistic is 4.4, making inflation an explanatory factor of oil price increases. However, inflation only explains 38% of the variation, according to the R-square value. Gasoline Pri...