1 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Vehicle Sales in the United States of America: A Statistical Analysis NAMES REMOVED University of South Alabama 2 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Abstract This paper examines a number of variables and their impact on vehicle sales in the United States (U.S.). It examines historic trends of the price of oil, U.S. Dollar and Euro exchange rates, the U.S. Federal Fund Rate, and total vehicle sales. A series of hypotheses are presented and tested utilizing the data collected for each variable. Statistical analyses, both descriptive and inferential, were performed to determine any significant impact these variables have on each other and on total vehicle sales in the U.S. Results of the analyses are presented in both table and graph forms. A discussion of the results and analyses reveals any significant findings of the project as well as reasons for further analyses and usage of the collected data with the subsequent analyses. 3 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Vehicle Sales in the United States of America: A Statistical Analysis In the United States you cannot go anywhere and not see a vehicle. According to I. Wagner (2020), “In the fourth quarter of 2019, there were some 279.6 million vehicles operating on the roads.” Vehicle sales in the United States occur daily—but to what extent do other factors affect, or rather, not affect the total number of vehicle sales in the United States? This project will discuss how oil prices, the Effective Federal Funds Rate, and the U.S. Dollar/Euro exchange rate affect the total number of vehicle sales. Background While other forms of energy exist, most cars still use gasoline as fuel, so one variable that may affect how many vehicles are sold in the United States is the price of oil per barrel. The first null hypothesis discussed in this project is that oil prices do not predict the outcome of total vehicle sales in the United States, with an alternative hypothesis stating that oil prices predict the outcome of total vehicle sales in the United States. The null suggests that regardless of the price of oil, total vehicle sales will not be impacted. Therefore, an increase in the price of oil per barrel will not significantly increase or decrease the number of vehicles sold in the United States. We predict that this will not be the case, and that oil prices can be used to predict the number of vehicles sold in the U.S. The Effective Federal Funds Rate determines the interest rate on money that is traded between banks on a nightly basis to maintain a certain level of cash in their accounts (FRED, 2020). Because banks often give personal loans to people in order for them to purchase vehicles, our second null hypothesis is that the Effective Federal Funds Rate does not predict the outcome of total vehicle sales in the United States with an alternative hypothesis stating that the Effective 4 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Federal Funds Rate does predict the outcome of total vehicle sales in the United States. The null for this hypothesis implies that changes in the Effective Federal Funds Rate do not significantly change the number of vehicles sold in the United States. We believe that this is not the case and that the Effective Federal Funds Rates will have an impact on the total number of vehicles sold. When the European currency (Euro) is exchanged for the U.S. Dollar, the value of the dollar increases or decreases depending on the current exchange rate. This exchange rate could potentially be used to predict how vehicle sales will do in the United States, especially when the number of vehicles imported from Europe is considered. The third null hypothesis discussed in this paper is that U.S. Dollar/Euro exchange rates do not predict the outcome of the total vehicle sales in the United States, with an alternative hypothesis that U.S. Dollar/Euro exchange rates do predict the outcome of total vehicle sales in the United States. We believe that the U.S. Dollar/Euro exchange rate will have a significant impact on the total number of vehicles sold in the U.S. As discussed previously, we believe that oil prices, the Effective Federal Funds Rate, and the U.S. Dollar/Euro exchange rate all individually predict how many vehicles are sold in the United States. We will now test the effect of all three variables on total vehicle sales simultaneously to determine whether they significantly impact total vehicle sales when combined. We believe this to be the case. Therefore, our null hypothesis is that oil prices, the Effective Federal Funds Rate, and the U.S. Dollar/Euro exchange rate do not predict the outcome to total vehicle sales. This leaves our final alternative hypothesis to be that oil prices, the effective federal funds rate, and U.S. Dollar/Euro exchange rate do predict the outcome of total vehicle sales. 5 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Previously, we were interested in whether these variables had a significant impact on total vehicle sales in the U.S. Now, however, we would like to determine whether a significant relationship between monthly oil prices and total vehicle sales in the U.S. exists. Our null hypothesis states there is no significant relationship between oil prices and total vehicle sales in the U.S. Oppositely, our alternative hypothesis states that there is a significant relationship between the two. We believe the alternative hypothesis to be true and that there is indeed a significant relationship between oil prices and total vehicle sales in the U.S. It has previously been discussed that we predict that the U.S. Dollar/Euro exchange rate does indeed impact the total number of vehicle sales in the U.S. We additionally would like to explore whether there a significant relationship exists between the two. We believe that there is a significant relationship between the U.S. Dollar/Euro Exchange Rate and total vehicle sales. As such, our null hypothesis is that a significant relationship does not exist between the U.S. Dollar/Euro exchange rate and total vehicle sales in the United States. The alternative hypothesis is that a significant relationship does exist between the U.S. Dollar/Euro exchange rate and the total number of vehicles sold in the United States. Method The project utilizes the Federal Reserve Economic Data (FRED) website in order to gather information about chosen variables. FRED compiles data from numerous sources and allows users to quickly and easily view trendlines of the chosen variable. This website is extremely valuable when attempting to compare economic data as it allows the user to manipulate the frequency, period, and units that the data set uses. This is useful in order to ensure 6 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS all variables compared in the project were collected over the same time period and with the frequency. This project compares monthly values from 01/01/2003-12/01/2019 for the following variables: oil prices per barrel, total vehicle sales (in millions), Effective Federal Funds Rate, and U.S. Dollar/Euro exchange rate. Using these values over a 17-year span, the data set includes 204 values for each of the five variables. This brings the total number of observations to 1,020. To better understand the data, the source and collection method need to be given. First, the oil price per barrel was based on the “West Texas Intermediate (WTI) - Cushing, Oklahoma” model. This is the preferred measure and pricing model in the United States according to the U.S. Energy Information Administration. FRED collected this data from the U.S. Energy Information Administration. Second, the total vehicle sales data was collected from the U.S. Bureau of Economic Analysis. Next, the Effective Federal Funds Rate is calculated as a “volume-weighted median of overnight federal funds transactions” (FRED, 2020), which FRED collected from the Federal Reserve Bank of New York. Lastly, the U.S. Dollar/Euro exchange rate is the noon buying rates in New York City for cable transfers payable in foreign currencies. FRED compiled this data from the Board of Governors of the Federal Reserve System. Initial Results Since the data level for all variables in question is in ratio, mean and median are used to describe the initial results and standard deviation is used as a measure of variability, as seen below in Table 1. 7 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Table 1 Mean, Median and Standard Deviation per Variable Mean, Median and Standard Deviation per Variable Variable Mean Median Standard Deviation Total Vehicle Sales 15.89 16.89 2.36 Oil Prices 67.81 63.58 23.60 Effective Federal Funds Rate 1.41 0.91 1.63 U.S. Dollar/Euro Exchange Rate 1.26 1.27 0.12 From an evaluation of the values computed for total vehicle sales, it is observed that the mean is located to the left of the median, which is an indication that the distribution is skewed. The skewed distribution can be observed on the following histogram in Graph 1 8 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Graph 1 Histogram for Total Vehicle Sales Performing the same analysis of the mean and median for oil prices and Effective Federal Funds Rate, as seen in Graphs 2 and 3, it is observed that the mean is located to the right of the median, therefore an indication that the distribution is rightly skewed. Graphs 2 and 3 Histograms for Oil Prices and Effective Federal Funds Rate The histogram for oil prices shows a slightly rightly skewed distribution while the respective for Effective Federal Funds Rate is highly skewed to the same direction. 9 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS From an analysis of the U.S. Dollar/Euro exchange rate, it is observed that the mean and median are relatively equal, an indication of a normal distribution. The histogram in Graph 4, however, shows that the distribution is rightly skewed. Graph 4 Histogram for U.S. Dollar/Euro Foreign Exchange Rate Although it is important to analyze how the data is distributed, the main purpose of this research is to learn the impact of oil prices, U.S. Effective Federal Funds rates, and the U.S. Dollar/Euro exchange rate on total vehicle sales. Based on that, the following Graphs were computed. Graph 5 shows the distribution of Total Vehicle Sales and Oil Prices. Graph 6 shows the distribution of Total Vehicle Sales and the Effective Federal Funds Rate and Graph 7 shows the distribution of Total Vehicle Sales and the U.S. Dollar/Euro Exchange Rate. 10 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Graph 5 Total Vehicle Sales vs Oil Price 2003-2019 Graph 6 Total Vehicle Sales and Effective Federal Funds Rate 2013-2019 11 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Graph 7 Total Vehicle Sales vs U.S. Dollar/Euro Exchange Rate 2003-2019 From the graphs presented above, it is possible to observe an indication of a relationship between the variables and the vehicle sales, more specifically an indication of an indirect relationship. As the value of total vehicle sales increases over time, the oil price, Effective Federal Funds Rate, and U.S. Dollar/Euro exchange rate decreases; and as total vehicle sales decrease, the other variables increase. Graph 5 can be explained as the price of oil increases, the less affordable it would be for most people to purchase a vehicle; therefore, the sales of vehicles would decrease. Similarly, the lower the price of oil, the more affordable it would be to have and maintain a vehicle. Therefore, the total vehicles sales increases. Graph 6 would follow the same stream of thought. As most people use personal loans from banks to purchase a vehicle, consequently a higher Effective Federal Funds Rate would result in a decrease of vehicle sales. 12 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Lastly, it is possible that the exchange rate between the U.S. Dollar and Euro could affect the sale price of European vehicles. The higher the exchange rate, the higher the price of the vehicle in the U.S. would be and could result in a decrease of vehicle sales. Even though, by observing the graphs, we have an indication of all the mentioned relationships, it is inaccurate to conclude those as significant without further analysis. Therefore, the statistical analyses on the possibility of oil prices, Effective Federal Funds Rates, and U.S. Dollar/Euro Foreign exchange rates impacting total vehicle sales are presented in the following sections. Results We will be using a type of inferential statistics called linear regression to identify whether there is a linear relationship between the predictor variables and outcome variable. Our predictors are oil prices, Effective Federal Funds Rates, and U.S. Dollar/Euro foreign exchange rates and our outcome is total vehicle sales in the U.S. Regression can also identify the “relatedness of one or many predictor variables with a single outcome” (Howard, 2020). For the purpose of this paper, we will be conducting regression analysis to test the following alternative hypotheses and their respective null hypotheses: HA1: Oil prices predict the outcome of total vehicle sales in the U.S. (Testing 1). HA2: Effective Federal Funds Rates predict the outcome of total vehicle sales in the U.S. (Testing 2) HA3: U.S. Dollar/Euro foreign exchange rates predict the outcome of total vehicle sales in the U.S. (Testing 3) 13 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Additionally, we will be examining each of the aforementioned relationships while controlling for the other predictors by utilizing multiple regression. Lastly, this paper will look at the following hypotheses tested by conducting the correlation analyses: HA4: A significant relationship exists between oil prices and total vehicle sales in the U.S. (Testing 4) HA5: A significant relationship exists between the U.S. Dollar/Euro foreign exchange rates and total vehicle sales in the U.S. (Testing 5) It is to be noted that correlation analysis is similar to regression analysis; however, they differ in that correlation measures the degree of a relationship between two variables, whereas regression typically measures how one variable, the predictor, affects the outcome variable. Testing 1: HA1: Oil prices predict the outcome of total vehicle sales in the U.S. H01: Oil prices do not predict the outcome of total vehicle sales in the U.S. Based on Graph 8, one can conclude that there is an implication that oil prices play a role in predicting total vehicle sales in the U.S. However, just by looking at the graph without analyzing the equation at all, the direction of the trendline shows there is a weak and negative relationship between oil prices and total vehicle sales. Looking closer at the equation itself, the slope is -0.381, which is indeed closer to 0 and signals a flatter trendline. 14 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Graph 8 Total Vehicle Sales 2003-2019 Our R2 of 0.145 confirms this weak link between the independent variable predicting our outcome. Our p-value of less than 0.05 helps us determine that we should reject our null hypothesis H01. We can also determine that the relationship is statistically significant and conclude that oil prices predict the outcome of total vehicle sales in the U.S. as seen in below Tables 2 and 3. Table 2 Model Fit Measures R R2 0.381 0.145 15 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Table 3 Model Coefficients - Total Vehicle Sales (Millions on Units) Predictor Estimate p Intercept 18.472 < 0.001 Oil Prices (Dollars per Barrel) -0.038 < 0.001 Testing 2: HA2: Effective Federal Funds Rates predict the outcome of total vehicle sales in the U.S. H02: Effective Federal Funds Rates do not predict the outcome of total vehicle sales in the U.S. The second regression analysis gives us a result that describes how well the Effective Federal Funds Rate predict the outcome of total vehicle sales in the U.S. With our slope being 0.479, we can conclude that there is a positive, but relatively flat regression. Our R2 value of 0.109 also helps confirm this. Like the first hypothesis testing above, a p-value of less than 0.05 in this caseallows us to reject the null hypothesis and determine that it is statistically significant. We can therefore conclude that Effective Federal Funds Rates significantly predict the outcome of vehicle sales in the U.S.as seen below in Tables 4 and 5. 16 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Table 4 Model Fit Measures R R2 0.330 0.109 Table 5 Model Coefficients - Total Vehicle Sales (millions of units) Predictor Estimate p Intercept 15.215 < 0.001 Effective federal fund rates 0.479 < 0.001 Testing 3: HA3: U.S. Dollar/Euro foreign exchange rates predict the outcome of total vehicle sales in the U.S. H03: U.S. Dollar/Euro foreign exchange rates do not predict the outcome of total vehicle sales in the U.S. The last linear regression analysis gives us a result that describes how well the U.S. Dollar/Euro foreign exchange rates predict the outcome of total vehicle sales in the U.S. With our slope being -11.8, we can conclude that this regression is a negative and rather steep. Our R2 value of 0.372 tells us that U.S. Dollar/Euro foreign exchange rates have a medium effect on the outcome of total vehicle sales in the U.S. A p-value of less than 0.05 in this case means that it is 17 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS statistically significant and signals us to again reject the null hypothesis. We conclude that U.S. Dollar/Euro foreign exchange rates predict the outcome of vehicle sales in the U.S. as seen below in Tables 6 and 7. Table 6 Model Fit Measures R R2 0.610 0.372 Table 7 Model Coefficients - Total Vehicle Sales (millions of units) Predictor Estimate p Intercept 30.80 < 0.001 U.S. Dollar/Euro Foreign Exchange Rate -11.8 < 0.001 All three hypothesis tests above have looked at how each predictor variable individually affects the total vehicle sales in the U.S. Multiple regression will assess how all of the predictor variables affect our only outcome, which is total vehicle sales in the U.S., while controlling for the other predictors. We can see that all three predictor variables are statistically significant in terms of predicting the outcome of total vehicle sales in the U.S. while controlling for the others, meaning that they all contribute to predicting the outcome variable. An R2 of 0.541 of the 18 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS multiple regression shows that the effect is moderate and greater than each individual R2 value of all the previous analyses. We can state that when accounting for the effect of all the predictors at the same time, we get a stronger predicting effect on the outcome as seen below in Tables 8 and 9. Table 8 Multiple Regression - Model Fit Measures R R2 0.735 0.541 Table 9 Model Coefficients - Total Vehicle Sales (millions of units) Predictor Estimate p Intercept 35.9859 < 0.001 Oil prices 0.0334 < 0.001 Effective Federal Funds Rates 48.0875 < 0.001 U.S. Dollar/Euro exchange rates -1749.5607 < 0.001 19 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Testing 4 & Testing 5: HA4: A significant relationship exists between oil prices and total vehicle sales in the U.S. H04: A significant relationship does not exist between oil prices and total vehicle sales in the U.S. HA5: A significant relationship exists between the U.S. Dollar/Euro foreign exchange rates and total vehicle sales in the U.S. H05: A significant relationship does not exist between the U.S. Dollar/Euro foreign exchange rates and total vehicle sales in the U.S. Table 10 Correlation Matrix Oil Prices and U.S. Dollar/Euro Exchange Rates Total vehicle sales Pearson’s r p Oil prices U.S./Euro exchange rates -0.381 <0.001 -0.610 <0.001 Based on the above correlation matrix in Table 10, total vehicle sales in the U.S. and oil prices have a correlation of -0.381 that is statistically significant with a p-value of less than 0.05. We can therefore reject the null hypothesis H04 and conclude that there is a significant relationship between total vehicle sales in the U.S. and oil prices. Likewise, total vehicle sales in the U.S. and U.S. Dollar/Euro exchange rates have a correlation of -0.610 and the relationship is also statistically significant with a p-value of less than 0.05. We can therefore reject the null hypothesis H05 and conclude that there is a significant relationship between total vehicle sales in the U.S. and U.S. Dollar/Euro exchange rates. 20 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS Discussion In Graph 1, we see a visual representation of the impact that oil prices have on total vehicle sales in the United States. There is only a slight, negative slope that can be seen when the data is plotted. Without doing any further analyses, it appears as though oil prices would not be a very good predictor of vehicle sales. In running a regression analysis on this same data, the impact of oil prices on vehicle sales was found to be statistically significant. This allows us to reject the null hypothesis and find that oil prices do have a significant impact on vehicle sales. Additionally, our slope was found to be -0.381 which confirms the negative impact oil prices have on vehicle sales. These analyses are important for two reasons. The first being that though a predictor’s impact may look weak visually, it does not mean said impact is insignificant—and vice versa. This is also important because experts/managers in the vehicle industry will most likely need methods of estimating sales volumes for the following financial period. Because we can show that oil prices are, statistically speaking, indeed a trustworthy predictor of vehicle sales, one could follow the trends in oil prices to forecast vehicle sales. For the following two tests, two and three, we follow similar logic. In Test 2, we ran a regression analysis to determine whether Effective Federal Funds Rates had a significant impact on total vehicle sales in the U.S. In this case, our slope was positive at 0.479 which tells us that as the Effective Federal Funds Rate increases, total vehicle sales should go up as well. Similar to oil prices, the R2 value in Test 2 was only 0.109—indicating that Effective Federal Funds Rate may not be a considerable predictor of vehicle sales in the U.S. However, the p-value of this test was found to be less than 0.001 and thus, we can determine the impact of Effective Federal Funds Rate on total vehicle sales is significant. This may be another variable managers and experts utilize when they are looking to forecast vehicle sales. Test 3 was used to determine whether U.S. Dollar/Euro foreign exchange rates are a statistically significant predictor of total 21 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS vehicle sales in the United States. The R2 value for this test was 0.372 and the slope was -11.8. Both values indicate that U.S. Dollar/Euro foreign exchange rates are a very good predictor of total vehicle sales—though it is a negative relationship. The p-value supports this finding as well, being that it is less than .001. Professionals in the vehicle industry may use this variable to estimate vehicle sales. In the previous section, we ran individual regression analyses on the effect that oil prices, the Effective Federal Funds Rate and U.S. Dollar/Euro foreign exchange rates had on total vehicle sales in the United States. We found that all three predictors were significant predictors for vehicle sales with varying R2 values. These values explain what percent of variance in total vehicle sales our predictor variable is responsible for. In this section, we wanted to know how much of the variance in total vehicle sales was determined by all three of our predictor variables. In order to do so, we ran a Multiple Regression analysis in which all three variables (oil prices, the Effective Federal Funds Rate and U.S. Dollar/Euro foreign exchange rates) were our predictors, and total vehicle sales was the outcome variable. We found that all three variables had p-values of less than .001, meaning that they are all significant predictors of total vehicle sales once again. The R2 value came out to be 0.541 which tells us that these three variables can explain approximately 54% of the variance in total vehicle sales. This is a considerable amount of variance in the outcome explained and supports our alternative hypotheses that these three variables do significantly impact total vehicle sales. The last two analyses we ran on this data were for correlations that may exist within the variables. Our first correlation hypothesis states that a significant relationship exists between oil prices and total vehicle sales in the U.S. Our analysis found a correlation of -0.381 between the two. This relationship can be described as a negative, moderate relationship—similar to our 22 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS findings when running a regression analysis. This would mean that as oil prices increase, total vehicle sales will fall, and vice versa. Our p-value for this analysis was less than .001, meaning that a significant relationship does exist between oil prices and total vehicle sales. Though this correlation does not prove any causation, this inverse relationship is very logical if we relate it to real-world contexts. The cheaper oil is, the cheaper it will be to make, transport and fuel vehicles in the U.S. A lower Cost of Goods Sold should result in a lower price tag for the vehicles, and a higher purchasing power for end users. Thus, a decrease in oil prices should increase vehicle sales for the United States. The second correlation we tested was whether a significant relationship exists between the U.S./Euro foreign exchange rates and total vehicle sales. Similar to oil prices, the exchange rates and vehicle sales had a negative correlation at -0.610. Though both correlations are negative, the correlation between U.S. Dollar/Euro foreign exchange rates is far stronger. This would suggest a more direct relationship between the variables, meaning U.S. Dollar/Euro exchange rate activity more explicitly affects vehicle sales in the United States. This could possibly be due to the fact that the higher the exchange rate is, the more a vehicle will cost in the U.S. This will obviously have a negative effect on the number of vehicles being sold. Strong relationships like these are important for management personnel or experts in this field to consider when making decisions. It should be noted that these analyses are based on only one sample of data. In order to further support these findings, more samples of similar data should be collected and tested. The more analyses we can run on samples of relevant data, the further we can test the above hypotheses. If similar results were found after many more sets of data are compiled and 23 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS analyzed, these variables could reasonably be used to make forecasts about future vehicle sales in the United States. 24 VEHICLE SALES IN THE UNITED STATES OF AMERICA: A STATISTICAL ANALYSIS References Board of Governors of the Federal Reserve System (US), Effective Federal Funds Rate [FEDFUNDS], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/FEDFUNDS, October 4, 2020 Federal Reserve Economic Data: FRED: St. Louis Fed. (n.d.). Retrieved October 06, 2020, from https://fred.stlouisfed.org/ Howard, M. (n.d.). Dr. Matt C. Howard. Retrieved October 06, 2020, from https://mattchoward.com/ U.S. Energy Information Administration - EIA - Independent Statistics and Analysis. (n.d.). Retrieved October 06, 2020, from https://www.eia.gov/todayinenergy/detail.php?id=43875 Wagner, I. (2020, May 14). U.S. - Number of Vehicles in Operation in the United States between 1st Quarter 2016 and 4th Quarter 2019. Retrieved October 04, 2020, from https://www.statista.com/statistics/859950/vehicles-in-operation-by-quarter-united-states/