Presented by:Alex Kelson, Ben Sparks, Drew Walsh, Oyebola Akinmulero, Shaghayegh Tareh, Tim Pearson, Tina Tran

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Table of Contents1. Find a statistical question to answer

• Located on Page 32. Come up with your own hypothesis

• Located on Page 3 3. Collect data

• Raw Data Located on Page 4 (Table 1 and Graph 1)4. Organize and summarize the data

• Located on Pages 5-65. Plot x vs. y and calculate linear correlation coefficient, r

• Located on Page 76. Predicted Y

• Located on page 8 Residual

• Located on page 97. Check to see if the linear model assumption is valid

• Located on Page 108. Make a few predictions

• Located on Page 119. Afterthought

• Located on Page 12 Sources

• located on page 13

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Statistical AnalysisIs there a correlation between the miles on a used Toyota

Corolla LE and the asking price at a used car dealership?

We believe that there is a linear correlation where more miles that a used Toyota Corolla LE has the lower the sticker or asking price will be at the used car dealership.

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Data on Toyota Corolla LEMileage (X) Price (Y)

37616 $18,32630695 $17,49435461 $17,07945233 $16,94131727 $15,99039797 $15,69045721 $15,69041454 $15,49036589 $15,29039775 $14,87740547 $14,35940881 $14,35940957 $14,35952171 $14,29033371 $14,00034571 $13,99848691 $13,71543353 $13,65636162 $13,57771259 $12,99570936 $12,99038210 $11,99596495 $10,99987974 $10,990

115085 $10,59682190 $10,44488727 $10,00096962 $8999

102618 $8995109529 $7977

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Table 1 Graph 1

Dataset X (mileage) Column n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3

MILEAGE 30 57158.566 7.2311782E8 26890.85 4909.575 42403.5 84390 30695 115085 37616 82190

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Dataset Y (Price)Column N Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3

PRICE 30 13545.333 7218841.5 2686.7903 490.53854 13999 10349 7977 18326 10999 15690

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Best Fit Line and Correlation Coefficient

Y=-0.0859x +18450R=.8615683374

20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 1200000

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

f(x) = − 0.0859161701476238 x + 18449.5118057943R² = 0.742325122545443

Graph 2

MILES

PRICE

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Calculations and Graph for Predicted Y• Predicted Y vs X

• To get predicted Y we plug Observed X from Table 2 into the Best Fit Line Equation of Y=-0.0859x +18450. (Graph 3)

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Table 2

20000 40000 60000 80000 100000 120000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Calculations and Graph for ResidualObserved X Observed Y Predicted Y Residual

37616 18326 15218.7856 3107.214430695 17494 15813.2995 1680.700535461 17079 15403.9001 1675.099945233 16941 14564.4853 2376.514731727 15990 15724.6507 265.349339797 15690 15031.4377 658.562345721 15690 14522.5661 1167.433941454 15490 14889.1014 600.898636589 15290 15307.0049 -17.004899999939775 14877 15033.3275 -156.32749999940547 14359 14967.0127 -608.01269999940881 14359 14938.3221 -579.32209999940957 14359 14931.7937 -572.793752171 14290 13968.5111 321.488933371 14000 15583.4311 -1583.431134571 13998 15480.3511 -1482.351148691 13715 14267.4431 -552.443143353 13656 14725.9773 -1069.977336162 13577 15343.6842 -1766.684271259 12995 12328.8519 666.148170936 12990 12356.5976 633.40239999938210 11995 15167.761 -3172.76196495 10999 10161.0795 837.920587974 10990 10893.0334 96.966599999

115085 10596 8564.1985 2031.801582190 10444 11389.879 -945.8790000088727 10000 10828.3507 -828.3506999996962 8999 10120.9642 -1121.9642

102618 8995 9635.1138 -640.113799999109529 7977 9041.4589 -1064.4589

Residual vs. X

PRICE

MILES 9

Graph 4

Table 2

• Residual • To produce the residual we subtract

the Observed Y from the Predicted Y in Table 2 . This produces Graph 4.

Linear Model Assumption

Due to the fact that there is a linear correlation using the best fit line model we have met the criteria for section A on #7Since there was no discernible pattern in the graph of “Residual vs X” (found on Page 8), the data is linearly related.

Since we have used 30 points in our data set and our correlation coefficient or R =.8615 this is much higher than the required .361 we have found a strong positive correlation.

We have concluded that using the data from cars.com, a strong correlation between the miles on a used vehicle will lower the sticker/asking price of a Toyota Corolla LE. 10

Predictions Using Equation

To get predictions we come up with X that is within the ranges of our data and plug it into the Best Fit Line Equation of Y=-0.0859x +18450

X Y30000 1587335000 15443.540000 1501445000 14584.550000 1415555000 13725.562500 13081.2570000 1243775000 12007.580000 1157885000 11148.590000 1071995000 10289.5

100000 9860

Predicted using Equation

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Graph 5

Table 3

After Thought• Did you just do a convenience or voluntary-response sampling to collect your data?

The sampling data was convenience based. We found it through an internet search.

• Did your study suffer from too few data points? We don’t believe the study suffered from too few data points, it points out clearly that car value decreases with increased mileage.

• Are you misrepresenting the data? No we are not misrepresenting the data.

• Is your analysis correct? The analysis is correct.

• Does your conclusion make sense? Yes our conclusion makes sense.

• We believe that the study was useful for our reader. However, most of this knowledge is considered common sense. We think it would have been helpful to research a variety of cars and compare resale value based on mileage. This study could have more value by comparing upgrades vs. stock resale value and this could be done for multiple makes and models. This could influence the reader’s decision between makes and models and the upgrades purchased depending on the added resale value.

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Sources• All statistical data was acquired using the Cars.com search

engine for “Used Toyota Corolla LE” search grid within 10 miles of 84070 accessed on 11/14/11 http://www.cars.com/for-sale/used/toyota/corolla/le/_/N-ma9Zfi0Zg3hZinqZm5d?sf1Dir=DESC&mkId=20088&mdId=20861&rd=10&zc=84070&PMmt=1-1-0&stkTypId=28881&sf2Dir=ASC&sf1Nm=price&sf2Nm=miles&rpp=50&feedSegId=28705&searchSource=GN_REFINEMENT&crSrtFlds=stkTypId-feedSegId-mkId-mdId-trId&pgId=2102&trId=24182

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