Building SPEED What Makes a Track Fast? What Makes a Track Fast? Tracks on the NASCAR circuit are measured using multiple attributes. Statistics can range from length of track, banking degrees in curves, average speed of laps, width of lanes, to many other features. When sifting through all of those numbers, how do we decide which tracks are truly the fastest? Let’s use the following data: Track Name Length of track Banking Fastest Lap in (in miles) (in degrees) 2010 (mph) 1 Atlanta Motor Speedway 1.54 24 192.761 2 Auto Club Speedway (Fontana, CA) 2 14 185.285 3 Bristol Motor Speedway .533 30 124.630 4 Charlotte Motor Speedway 1.5 24 191.544 5 Chicagoland Speedway 1.5 18 183.542 6 Darlington Raceway 1.366 24 180.370 7 Daytona International Speedway 2.5 31 191.188 8 DoVer International Speedway 1 24 157.315 9 Homestead-Miami Speedway 1.5 20 176.904 10 Indianapolis Motor Speedway 2.5 9 182.278 11 Kansas Speedway 1.5 15 174.644 12 Las Vegas Motor Speedway 1.5 20 188.719 13 MartinsVille Speedway .526 12 97.018 14 Michigan International Speedway 2 18 189.984 15 New Hampshire Motor Speedway 1.058 12 133.572 16 Phoenix International Speedway 1 10 136.389 17 Pocono Raceway 2.5 9 171.393 18 Richmond International Raceway .750 14 127.077 19 Talladega Superspeedway 2.66 33 184.640 20 Texas Motor Speedway 1.5 24 195.397 This data has three components: Length of Track: This is the total length of one revolution around the track Banking: This is the degree of banking in the steepest portion of the track Fastest Lap in 2010: This is the fastest speed of the driver during their qualifying laps that landed the pole position at one of the races held at the track in the 2010 season. If there was racing at the same track twice during 2010, then the fastest lap was chosen. Page | 1 Building SPEED What Makes a Track Fast? Exploration Questions: 1. From the data given, which track appears to be the fastest and why? Which track appears to be the slowest and why? 2. A confounding variable is an outside variable beyond the control of the race teams and officials. What are some confounding variables that could contribute to the speed of the tracks? 3. Describe in your own words how the track’s “banking” affect the speed of the cars. 4. Compare the statistics for Martinsville Speedway and Pocono Speedway. Why is the fastest speed for Martinsville lower than Pocono even though Pocono has lower banking? Page | 2 TI-8TI3 -8Symb3 Symbol Folon Ftsonts DownloadDow fontnload from font: ht tfp:rom//educat: http:/i/on.educatti.comion./educatti.comi/onporeducattalionpor/appsdeltal/appsdelivery/dowivernload/y/dowdownload/nload_edowTInlul-8oad_ea.jsp?app3ul Sa.jlsiymbcp?appationIld=61icatolionI79& d=61Fconton79&entPctsaneIontentd=13PaneI&cid=13d=US&cid=US Download font from: http://educatShiion.ft t(CShii.comaftps/educat (C) apsionpor) tal/appsdelivery/download/download_eula.jsp?applicationId=6179&contentPaneId=13&cid=US Shift (Caps) ~ ~ ! ! @ @ # # $ $ % % ^ ^ & & * * ( ( ) ) _ _ + + ~ ! @ # $ % ^ & * ( ) _ + Q Q W W E E R R T T Y Y U U I I O O P P { { } } | | Q W E R T Y U I O P { } | A A S S D D F A F G S G H D H JF J GK K HL L :J : “ K “ L : “ Z Z X X C C V Z V B X B NC N VM MB< < >N > ?M ? < > ? NormNalo kremysal keys Normal keys ` ` 1 1 2 2 3` 3 4 1 4 5 2 5 6 3 6 7 4 7 8 5 8 96 9 07 0 -8 - =9 = 0 - = q q w w e e rq r t w t y e y u r u i t i o y o pu p [i [ ]o ] \p \ [ ] \ a a s s d dBuilding SPEEDf a f g s g h d h j f j k g k l h l ;j ; ‘k ‘What Makes a l ; Track Fast?‘ z z x xUsec yourc vGraphingz v b x Calculatorb n c n andmv followm , bthe ,directions.n . givenm/ /to answer, the. next / questions: ExtenExdtenedd Ched araChctersaraExtenctersded Characters (These(These characte charrsacte are rsac arcessee (Theseacdcesse by holdingchard byacte holding downrs are down theaccesse “Alt” thed “Alt”bykey holding then key ty then pingdown ty theping the numbers “Alt”the numbers ke ony thenthe on numer ty theping numeric the key numbersic pad.) key pad.) on the numeric key pad.) Enter the data for the tracks into your calculator using the following instructions: a. Press , and choose 1: Edit. Be sure to clear out any existing lists. b. Under d, enter the track number c. Under e, enter the track length d. Under f, enter the track banking e. Under g, enter the track speed Next, we want to determine if there is a correlation between the banking of the track and the maximum speed of the track. Using the following instructions, graph the scatterplot of this data: a. Press y , o, , (this should highlight the “on” for Plot 1) b. Scroll down to highlight the selection for the XList and change it to f (which is our banking data) by pressing y , 3. c. Scroll down to highlight the selection for the YList and change it to g (which is our speed data) by pressing y, 4. d. Press q , 9. 5. Graph the scatterplot of your data below. Be sure to label each axis. Page | 3 TI-83 Symbol Fonts Download font from: http://education.ti.com/educationportal/appsdelivery/download/download_eula.jsp?applicationId=6179&contentPaneId=13&cid=US Shift (Caps) ~ ! @ # $ % ^ & * ( ) _ + Q W E R T Y U I O P { } | A S D F G H J K L : “ TI-83 Symbol Fonts Download font from: http://education.ti.com/educationportal/appsdelivery/download/download_eula.jsp?applicationId=6179&contentPaneId=13&cid=US Shift (Caps) Z X C V B N M <~ ! >@ # ? $ % ^ & * ( ) _ + Q W E R T Y U I O P { } | Normal keys TI-83 Symbol Fonts A S DownloadD font fromF: http://educatG ion.ti.comH /educationporJ tal/appsdelKivery/downlLoad/download_e: ula.jsp?app“ licationId=6179&contentPaneId=13&cid=US ` 1 2 3 4 5 6 7 8 9 0 - = Shift (Caps) ~ ! @ # $ % ^ & * ( ) _ + Z X C V B N M < > ? Q W E R TY U I O P { } | q w e r t y u i o p [ ] N\ormal keys ` 1 2 3 4 5 6 7 89 0 - = A S D F G H J K L : “ q w e r t y u i o p [ ] \ Z X C V B N M < > ? a s d f g h j k l ; ‘ Building SPEED What Makes a Track Fast? a s d f g h j k l ; ‘ Normal keys ` 6. Does1 there2 appear 3 to be a4 correlation5 between6 the7 banking8 degrees9 and0 the - = z x speed c of the vtrack? b Why orn why not?m If yes,, is the. correlation/ positive or z x c v b n m , . negative?/ q w e r t y u io p [ ] \ Extended Characters (These characters are accesse d by holdinga downs the d“Alt” kefy then tygping theh numbersj on the numerk ic keyl pad.) ; ‘ Extended Characters z x c v b n m , . / (These characters are accessed by holding down the “Alt” key then typing the numbers on the numer ic key pad.) Extended Chara cters (These characters are accessed by holding down the “Alt” key then typing the numbers on the numeric key pad.) Now, let’s determine a line of best fit for the data by following these directions: a. Press , right arrow to /, 4:LinReg(ax+b) b. The calc should now say “LinReg(ax+b )” and you need to tell it to compute the statistics based on f and g by pressing y, 3, , y, 4, . 7. What is the line of best fit for the banking and speed data? 8. There are many different guidelines for the interpretation of a correlation coefficient. It has been observed, however, that all such criteria are in some ways arbitrary and should not be observed too strictly. This is because the interpretation of a correlation coefficient depends on the context and purposes. What is a strong correlation for one situation may be weak in another situation. For example, a correlation of .9 may be very low if one is verifying a physical law using high-quality instruments, but may be regarded as very high in the social sciences where there may be a great contribution from complicating factors. Correlation Negative Positive Use the chart to the right to interpret the correlation for this set of data. What is the correlation Small −0.3 to −0.1 0.1 to 0.3 coefficient (r-value) for this data? Do you think this Medium −0.5 to −0.3 0.3 to 0.5 is a strong, moderate, or weak correlation? Describe Large −1.0 to −0.5 0.5 to 1.0 the relationship between these two numbers. (you may need to turn “Diagnostics” on) Page | 4 Building SPEED What Makes a Track Fast? 9. Using the information you haVe stored in your calculator and what you know about correlation coefficients, try to find a stronger relationship between two other Variables. Are there two Variables with a stronger correlation than banking and speed? If yes, what are they? 10. Discuss why you think the results of the question aboVe had that outcome.