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Alma Flores-PerezAP Statistics Per. 6Kiker9/27/13Does Car Length Affect Fuel Economy?This summer, my mom bought me a car. When buying said car, we took a lot of different factors into consideration. The first and most important factor we thought about was the fact that I would have to pay for my own gas. Obviously a car with better fuel efficiency wouldn’t waste as much gas and would therefore not cost me as much money. The second factor we took into consideration was the size of the car. While a larger car might be more safe, smaller cars would be easier to park and control on the road. We eventually decided on a FIAT 500 because it was the best of both worlds. It’s a small car that also has great gas mileage. Next I wondered if the size of all cars had an effect on their fuel efficiency, I decided to find out.Obviously, there are hundreds of different makes and models I could have chosen data points from, but I felt it would make the most sense if I went with some of the more common ones that I see around Austin. The 16 car brands that I chose were, Honda, FIAT, Hyundai, Nissan, BMW, Ford, Chevrolet, Mazda, Kia, Lexus, Toyota, Volkswagen, Volvo, Mercedes-Benz, Cadillac and Audi. Within each make, I chose two different models, usually one small car and one larger one. From each make’s website, I then collected the specifications on estimated highway fuel efficiency and overall car length. In this data set, I thought length would be the explanatory variable and fuel economy would be the response variable. By this I mean that I assumed that length would be a better predictor of fuel economy than vice versa. Once I collected all of my data, I plotted it into a scatterplot with the length range from 139.6-228.7 inches and the fuel economy range from 18-40 MPG (highway). On the scatterplot is desplayed the Least Squares Regression Line that best fit my collected data. If placed into y=a+bx form, the equation would be y=66.014-0.1963x. In my equation, the slope is -0.1963x. This means that for each additional increase in 1 inch, the fuel efficiency decreases by 0.1963 miles per gallon. The y-intercept for the equation is 66.014. This signifies that if the length of a car was 0 inches, the fuel economy of said car would be approximately 66.014 miles per gallon. The coefficient of correlation (r) for my data is -0.5326. This value shows that my regression is moderately strong, with a linear form, in the negative direction. The coefficient of determination (r2) for my data is 0.2837 or 28.37%. This means that 28.37% of the variation in fuel economy can be explained by the regression on car length. For a two-variable scatterplot, a point must be considered an outlier in both variables for it to be considered a true outlier. In order to find this, I used my TI-84 calculator to create modified boxplots for both of the variables. In the modified boxplots, it shows you which points are outliers in accordance with the 1.5 +/- IQR rule. In the explanatory variable axis, there were three outliers at 139.6 213.2 and 228.7 inches. In the response variable axis, there weren’t any outliers, meaning that those three points aren’t true outliers. The three points I checked to see if they were influential were the outlier points from the explanatory variable. Those three points were (139.6, 40), (213.2, 23) and (228.7, 20). An influential point would have a drastic effect on a rgression line when taken out. The three points I checked if they were influential were the three points that were outliers on the explanatory variable axis. When (139.6, 40) was taken out, the least-squared regression changed to y=64.0388-0.1859x with an r-value of -0.4589. The slope decreased as well as the y-intercept. The r and r2 values also decreased with the points excluded. When (213.2, 23) was taken out, the line of best fit changed to y=65.18-0.1915x with a coefficient of correlation of -0.5027. In this equation, the slope, y-intercept, r and r2 values also decreased. With the point (228.7, 20) excluded, the line of best fit changed y=64.5179-0.1879x with an r-value of -0.4634. All of the values in this equation also decreased. Due to only minor changes in the equation, I concluded that none of these values were influential points in the data.In a residual plot, the key things to look for are random scatter and no pattern. When I plotted the residual values for my data, They didn’t display any decernable pattern, meaning that the linear regression was one of the best fits for 0106680000this set of data. Next, I used my calculator to test all of the other types of regressions that it offers. There were three that had similar value for the coefficients of correlation and determination, but only one had higher values than a linear regression. The quartic equation that went with my data, had a coefficient of dtermination of 28.47%, which was only slightly more than that of a linear regression.According to my equation, a car with the length of 145 inches would have a fuel economy of approximately 37.5505 miles per gallon. The Mini Cooper has a length of 146.8 inches with a highway fuel efficiency of 37 MPG. If I input the exact length of a Mini, it’s estimated fuel efficiency would be 37.197 miles per gallon, which is almost exactly the actual value. The residual of this data point would be -0.197. It slightly overestimated the fuel economy value. Although the linear regression may not have been accurate for all of the data points, it did do an alright job of predicting the general trend.Although statistician isn’t a very common job, there are many out there that gather data like this and try to find relationships between two variables. One example of that type of career would be a marketing manager in a company. Their job would be to find what variables may be accounting for more sales or what factors people resond the best to. Another career would be meteorologists who find values of weather and what other rising or falling factors may affect certain weather patterns. This career helps predict what the weather may bring in the next few days or even the next few years.The data that I collected definitely showed some association between the overall length or a car and fuel economy in miles per gallon. It wasn’t the highest coefficient of correlation or determination, but there was association nonetheless. On the other hand, just because there was an association between the two variables, that doesn’t necessarily mean that car length alone is the cause of a car’s fuel economy. There may be other factors that have an effect of fuel efficiency, but in general, the length of car has some effect on it’s estimated fuel economy. Smaller gars usually get better gas mileage. Larger cars usually get worse gas mileage. My FIAT, the smallest length in the data set, also had the best fuel economy, leading me to believe that I made a good car choice.Works Cited"2013 F-150 Specifications."?. Ford, n.d. Web. 22 Sept. 2013."2013 X-Terra Specs."?Nissan USA. Nissan, n.d. Web. 22 Sept. 2013."2014 Fiat 500L Overview."?. FIAT USA, n.d. Web. 22 Sept. 2013."2014 Honda Odyssey - Specifications - Official Honda Site."?Automobiles.. Honda, n.d. Web. 22 Sept. 2013."2014 Mazda 6 Specifications."?. Mazda, n.d. Web. 22 Sept. 2013."The 2014 Rio- Specifications."?Kia Cars, SUVs, Crossovers, Minivans, & Future Vehicles. Kia, n.d. Web. 22 Sept. 2013."2014 RX Specifications."?Lexus: New Luxury Cars and SUVs from Lexus USA. Lexus, n.d. Web. 22 Sept. 2013."2014 Tahoe Models & Specs."?. Chevrolet, n.d. Web. 22 Sept. 2013."BMW 128i Coupe Features & Specs."?BMW USA. BMW, n.d. Web. 22 Sept. 2013."Compare Results."?Toyota Camry. Toyota, n.d. Web. 22 Sept. 2013."Hyundai Elantra Features."?. Hyundai USA, n.d. Web. 22 Sept. 2013. ................
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