Car Project
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Type of car: 2001 Honda Accord LX. Explanatory variable: age of car, response variable: asking price of the car. The two variables should be negatively associated, as the older the car is, generally the cheaper the car would sell. I think the relationship will be quite strong.
Observations: the differences in asking price are large when comparing relatively newer cars, and as cars get older, their age makes less of a difference in asking price.
We tried to get a good variety of the age and asking price for the car by picking offers with cars which are both very old and very new. We also chose a variety of locations where the car is sold, not just Minnesota, to get a good representation of the asking price of a Honda Accord LX.
The data of the scatter plot appears linear for the most part, except when the car age is approximately more than 12 years old, in which the data appears to trail off.
This is not a good model of the data because it only represents a small set of the overall data. There are cars with a much higher asking price and a much lower asking price that is not represented.
From the TI-83+ calculator, a more accurate equation of the least-squares line is Asking_price=-1155.919957Car_Age+18132.3677 We see that if we let Car_age be the mean value of our car age data, that is, car_age=7.06667, the asking price output as dictated by the equation is the mean value of our asking price data, that is,
Asking_price=9963.862817. We have r=-0.9334381494, which seems to be a good approximation of our data and just as what I predicted in the beginning (that the variables are negatively associated and have a strong correlation). We have r2=0.8713067787, which means that approximately 87.13% of the variation in the asking price can be explained by our least-squares regression line.
There doesn't appear to be any obvious outliers in our original plot, but we can see from the big picture that the residual plot has a sort of upward-opening parabolic pattern, possibly meaning that a linear regression may not be the best choice for approximating our function.
The value of the slope in the least-squares regression line is approximately -1155.92, which means that in our model, for every year added to the age of the car, its asking price decreases by $1155.92. This is not a fixed value for automobile selling prices, because the data will be different for other car types and models, this is only a model for the Honda Accord LX. The y-intercept in our least-squares regression line is approximately 18132.37, which means for our model of Honda Accord LX asking prices, a new car (year 2009) would have an asking price of $18132.37. This is somewhat close to the actual price, but it's still lower than the actual price of about $22225 in our data. Realistically, the predicted price would have been the asking price for an LX that's one or two years old. To use the least-squares regression line to predicted the asking price for a 2001 Honda Accord LX is as follows: the age of the car is 8, and we use the equation Asking_price=-1155.9199574368(8)+18132.36769922=8885.00804
Seeing that in our actual data, the asking price for a 8-year-old car ranges from near $9000 to approximately $7500, I think that the least-squares regression line prediction is more accurate than the mean price, which is 9963.87. This is because the least-squares regression line considers and explains more data than merely the mean. We see that our car age function has included a “0” as an element, thus we cannot apply any sort of logarithm to the car age set. Therefore we can only apply the natural log function to the asking price set and create an exponential regression. -The least-squares regression line of the natural log of the price set and the car age set is: ln(Asking_price)=-0.1569202967Car_age+10.11876442 Asking_price=e-0.1569202967Car_age+10.11876442 Asking_price=24804.10444*0.8547721843Car_age
Using this equation, we have the asking price for an 8-year-old car to be 7068.489222.
Car ads we used: 1. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5985561&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=1&certified=0 2. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5747339&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=1&certified=0 3. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5816905&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 4. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5988164&xdealerid=1406&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 5. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5842916&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 6. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5763666&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 7. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5509211&xdealerid=3550&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 8. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5846167&xdealerid=3864&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 9. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5616969&xdealerid=2580&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 10. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5661608&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=3&certified=0 11. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5683320&xdealerid=1908&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 12. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5746862&xdealerid=3658&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 13. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5680201&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=3&certified=0 14. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5766934&xdealerid=3923&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 15. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5547144&xdealerid=3150&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 16. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5369918&xdealerid=3313&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0&vc=1 17. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5616865&xdealerid=3313&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0&vc=1 18. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5804511&xdealerid=3372&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0
19. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5810807&xdealerid=2369&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0 20. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5617606&xdealerid=2384&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0&dealergroupid=42&vc=1 21. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5750762&xdealerid=2967&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0&dealergroupid=204 22. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5712488&xdealerid=2506&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =6&certified=0 23. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5845975&xdealerid=1646&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =7&certified=0 24. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5785244&xdealerid=3380&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =7&certified=0 25. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5814458&xdealerid=379&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 8&certified=0&dealergroupid=45 26. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5978813&xdealerid=566&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 9&certified=0 27. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5985810&xdealerid=1728&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =9&certified=0 28. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5734761&xdealerid=983&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 11&certified=0 29. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5648774&xdealerid=2441&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =12&certified=0 30. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5769735&xdealerid=557&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 1&certified=0&dealergroupid=32
Observations: the differences in asking price are large when comparing relatively newer cars, and as cars get older, their age makes less of a difference in asking price.
We tried to get a good variety of the age and asking price for the car by picking offers with cars which are both very old and very new. We also chose a variety of locations where the car is sold, not just Minnesota, to get a good representation of the asking price of a Honda Accord LX.
The data of the scatter plot appears linear for the most part, except when the car age is approximately more than 12 years old, in which the data appears to trail off.
This is not a good model of the data because it only represents a small set of the overall data. There are cars with a much higher asking price and a much lower asking price that is not represented.
From the TI-83+ calculator, a more accurate equation of the least-squares line is Asking_price=-1155.919957Car_Age+18132.3677 We see that if we let Car_age be the mean value of our car age data, that is, car_age=7.06667, the asking price output as dictated by the equation is the mean value of our asking price data, that is,
Asking_price=9963.862817. We have r=-0.9334381494, which seems to be a good approximation of our data and just as what I predicted in the beginning (that the variables are negatively associated and have a strong correlation). We have r2=0.8713067787, which means that approximately 87.13% of the variation in the asking price can be explained by our least-squares regression line.
There doesn't appear to be any obvious outliers in our original plot, but we can see from the big picture that the residual plot has a sort of upward-opening parabolic pattern, possibly meaning that a linear regression may not be the best choice for approximating our function.
The value of the slope in the least-squares regression line is approximately -1155.92, which means that in our model, for every year added to the age of the car, its asking price decreases by $1155.92. This is not a fixed value for automobile selling prices, because the data will be different for other car types and models, this is only a model for the Honda Accord LX. The y-intercept in our least-squares regression line is approximately 18132.37, which means for our model of Honda Accord LX asking prices, a new car (year 2009) would have an asking price of $18132.37. This is somewhat close to the actual price, but it's still lower than the actual price of about $22225 in our data. Realistically, the predicted price would have been the asking price for an LX that's one or two years old. To use the least-squares regression line to predicted the asking price for a 2001 Honda Accord LX is as follows: the age of the car is 8, and we use the equation Asking_price=-1155.9199574368(8)+18132.36769922=8885.00804
Seeing that in our actual data, the asking price for a 8-year-old car ranges from near $9000 to approximately $7500, I think that the least-squares regression line prediction is more accurate than the mean price, which is 9963.87. This is because the least-squares regression line considers and explains more data than merely the mean. We see that our car age function has included a “0” as an element, thus we cannot apply any sort of logarithm to the car age set. Therefore we can only apply the natural log function to the asking price set and create an exponential regression. -The least-squares regression line of the natural log of the price set and the car age set is: ln(Asking_price)=-0.1569202967Car_age+10.11876442 Asking_price=e-0.1569202967Car_age+10.11876442 Asking_price=24804.10444*0.8547721843Car_age
Using this equation, we have the asking price for an 8-year-old car to be 7068.489222.
Car ads we used: 1. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5985561&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=1&certified=0 2. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5747339&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=1&certified=0 3. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5816905&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 4. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5988164&xdealerid=1406&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 5. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5842916&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 6. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5763666&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=2&certified=0 7. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5509211&xdealerid=3550&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 8. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5846167&xdealerid=3864&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 9. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5616969&xdealerid=2580&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =2&certified=0 10. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5661608&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=3&certified=0 11. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5683320&xdealerid=1908&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 12. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5746862&xdealerid=3658&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 13. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5680201&makeid=31&minyear=192 0&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page=3&certified=0 14. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5766934&xdealerid=3923&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 15. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5547144&xdealerid=3150&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0 16. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5369918&xdealerid=3313&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0&vc=1 17. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5616865&xdealerid=3313&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0&vc=1 18. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5804511&xdealerid=3372&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =3&certified=0
19. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5810807&xdealerid=2369&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0 20. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5617606&xdealerid=2384&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0&dealergroupid=42&vc=1 21. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5750762&xdealerid=2967&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =4&certified=0&dealergroupid=204 22. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5712488&xdealerid=2506&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =6&certified=0 23. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5845975&xdealerid=1646&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =7&certified=0 24. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5785244&xdealerid=3380&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =7&certified=0 25. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5814458&xdealerid=379&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 8&certified=0&dealergroupid=45 26. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5978813&xdealerid=566&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 9&certified=0 27. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5985810&xdealerid=1728&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =9&certified=0 28. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5734761&xdealerid=983&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 11&certified=0 29. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5648774&xdealerid=2441&makeid= 31&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page =12&certified=0 30. http://myfox9.carsoup.com/used/detail.asp?usedvehicleid=5769735&xdealerid=557&makeid=3 1&minyear=1920&maxyear=2009&searchid=W136672&vehicletypeid=1&uvviewid=4&page= 1&certified=0&dealergroupid=32
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