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Econometrics

Econometrics Based on certain variables/factors, this mathematical analysis will attempt to create an equation that will predict the fuel economy of an automobile. The dependent variable used will be miles per gallon used on a highway. The “automobile” used for this analysis will include the 2 most popular 2002 models from every major auto brand on the American market. Popularity will be based on the number of units sold in a given year. In total, this analysis will use 68 different auto models The autos chosen will include one compact or midsize car and a Sports Utility Vehicle (SUV) or light truck. In the event an auto name does not have an SUV or light truck, another auto will be chosen and vice-versa. This analysis will not include commercial trucks (trucks with air brakes), buses, motorcycles and mopeds. The information needed for this analysis will be obtained from Carguides.AOL.com. All the specifications will be obtained for all brand new autos. Independent Variables: Cross Sectional Data Total Weight of the Automobile (Expected Negative Correlation): The weight of the automobile will be measured in pounds. The automobile will contain the least standard features and packages that are available to the public. Factors such as emissions systems, radios, AC systems and other luxuries add weight to the automobile; therefore this analysis will try to equalize each auto by selecting the most standard package of trim and accessories. Although this analysis will try to create a universal standing ground for the weight of the autos, a weakness still may be experienced due to the weight variations. The weight of the automobile is expected to have a negative correlation with the overall fuel economy. Logically, the heavier something is, the more energy (fuel) it takes to move that object; therefore the lower Miles Per Gallon. Number of Passenger Doors (Expected Negative Correlation): The number of passenger doors will be represented by a dummy variable. This analysis will recognize two-door, three-door and four-door automobiles. In this case, the definition of a door is any normal means in which a passenger enters the vehicle. This will not include hatchbacks, trunks or sunroofs. The variables representing this data will be the same number of doors. For example, the number “2” will represent a two-door vehicle and so on. The number of passenger doors is also expected to have a negative result on the dependent variable. The more doors, the bigger and heavier the automobile will be; therefore the more fuel it will consume and a lower Miles Per Gallon. Number of Cylinders in the Engine (Expected Negative Correlation): This variable will also be represented by dummy variables. The number of cylinders in the automobile’s engine will be four, six and eight. The variables representing the cylinders will be the same number. For example, a six cylinder engine will be represented by “6” and so on. This will further help simplify the analysis. The number of cylinders in the engine will have a negative correlation on the fuel economy variable. The more cylinders that engine has, the more fuel it will use; therefore the lower the Miles Per Gallon achievable. Engine Size in Liters (Expected Negative Correlation): This variable will be represented by the liter size of the engine. The liter size will vary from 1.8 to 5.9 liters. This information is easily obtained from an auto’s spec analysis The liter size of the engine is expected to have a negative correlation will MPG. The liter size represents how much fuel intake is injected into the engine. Therefore, if the liter size of an engine is high, then the miles per gallon of the engine should be negatively affected Make weight (lbs.) # of doors # of cyclinders engine size MPG Land Rover Discovery 3470 2 6 3.2 19 Land Rover Range Rover 2694 2 4 2 27 Weight (lbs.) # of doors # of cyclinders Engine Size MPG Mean 3662.323529 3.5 5.823529412 3.305882353 25.08823529 St. Deviation 913.0520811 0.85518611 1.326438127 1.131355329 5.009648285 Regression 4 1105.132462 276.28312 31.7969 2.088E-14 Residual 62 538.7182842 8.6890046 Coefficients Standard Err t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 35.780031 2.489470 14.372548 0.000000 30.803656 40.756406 30.803656 40.756406 Weight -0.000560 0.000462 -1.212809 0.229804 -0.001484 0.000363 -0.001484 0.000363 # of Doors 0.608012 0.451391 1.346972 0.182892 -0.294306 1.510329 -0.294306 1.510329 # of Cylinders 0.104902 0.638870 0.164200 0.870108 -1.172179 1.381983 -1.172179 1.381983 Liters -3.416311 0.755364 -4.522732 0.000028 -4.926261 -1.906360 -4.926261 -1.906360 MPG = 35.78 - .00056(Weight) + .608012(# of Doors) + .104902 (# of Cylinders) – 3.416311 (Liters) (.004462) (.451391) (.638870) (.755364) t = -1.212809 1.346972 .1642 -4.522732 Adjusted Multiple R Squared- Considering this is a cross-sectional analysis, an adjusted R squared (R squared adjusted for degrees of freedom) of .6511 is relatively strong. In a sense, this “goodness of fit” explains 65% of the variation. Although this output is strong, there are still other variables that can be added to create a stronger equation to predict MPG. T-Statistics- As noted above, the calculated T-Values range from –4.522 to 1.346972. The critical T-Value, assuming a 5% two-tail test with 63 degrees of freedom, results in an estimated 1.99 according to Table B-1 in Using Econometrics”. Therefore, since the critical value is less than all the calculated T-Values, we can reject the null hypothesis. F-Test- As reported from the regression results, the F value is 31.80. The critical F value, considering a 5% level of significance and 63 degrees of freedom, results in an estimated 2.53 according to Table B-2 in “Using Econometrics”. Therefore, since the critical value is less than the F-Value, we can reject the null hypothesis and conclude that the equation does indeed have a significant overall fit. Bibliography:

Word Count: 1504