What Car Should I Buy? Linear Correlation Project Joseph Bailey December 13 th 2012

Lamborghini Gallardo  Make: Lamborghini  Model: Gallardo  Style: Lamborghini Gallardo

Age & Price The car at 0 years old is worth $211,319 (y-intercept) and every year the car decreases $12,317 (slope) in value. The slope of the line is negative. The linear correlation coefficient is which is a very strong negative correlation between age and price. From this data it can be concluded that as the age of the car increases (x), the price of the car decreases significantly (y). Eighty-seven percent of explained variation in the price of the car is explained by the age of the car. So this means that 87% of the age of the car affects the price of the car while the other percentage is affected by other factors like wrecks and defective parts in the car.

Age & Mileage The car at 0 years has about miles on it (y-intercept), which is not valid because every new car starts off with 0 miles on since the domain of this graph is from (0,∞). But, Every year, the mileage increases by miles (slope). The slope is positive. The linear correlation coefficient is , which is a strong positive correlation. From this graph, you can conclude that as the age of the car increases (x), the mileage of the car also increases. Seventy- three percent explained variation in the mileage of the car is explained by the age of the car. So 73% of the age of the car affects the mileage of the car, while the other percentage is affected by other factors.

Mileage & Price The car at 0 years is worth about $189,892 (y-intercept). For every mile, the price of the car decreases by $3.6. The slope is negative. The linear correlation coefficient is , which is a strong negative correlation. From this graph, you can conclude that as the mileage of the car increases (x), the price of the car decreases. Seventy-five percent explained variation in the price of the car is explained by the mileage on the car. So 75% of the mileage on the car affects the price of the car, while the other percentage is affected by other factors like wrecks, and defective parts and things of that sort.

Most Useful Model Age & Price The model that shows the relationship between age and price is the most useful model from the three because it has the strongest correlation coefficient (-.9330) from all of the examples. It has a strong negative correlation; the model also shows that 87.1% of explained variation in the price of the car is explained by the age of the car, while the remaining percentage is caused by other factors. The two variables (age & price) are one of the most common ways that people choose to decide on which new car to purchase and to compare prices between vehicles.

My Predictions After one year off the lot, my car will be worth $199,012 which is $12,317 less than the original price. After three years, my car is worth $174,378, which is $36,951 less than the original price, and after five years, the car is worth $149,744 which is $61,585 less than the original price. From this data, it can be concluded that age can predict price, and vice versa. Every year the value of the car decreases by $12,317, which is why the graph has a strong negative correlation.

Investment or Expenditure The purchase of this car, is qualified as an expenditure. As the age of the car increases, the price of the car decreases, as the mileage of the car increases, the price of the car decreases, and as age of the car increases, the mileage also increases. From these models, it can be concluded that many factors affect the price of the car negatively. There are very few ways that this vehicle can gain value over time, over time, the value of the car continues to decline in a constant manner.