Toyota Corollas Cars Financial Calculations

Question: Describe about the Toyota Corollas Cars for Financial Calculations. Answer: 1. Given data set for the age of the used Toyota Corollas Cars and the respective advertised prices are as highlighted below: Age (yr) Price Advertised ($) 1 12995, 10950 2 10495 3 10995, 10995 4 6995, 7990 5 8700, 6995 6 5990, 4995 9 3200, 2250, 3995 11 2900, 2995 13 1750 Part A Scatter plot for the above data in order to define the relationship between the car prices and their respective ages is as illustrated below: Part B It is apparent from the above scatter plot that the given data illustrates a negative slope, which describes the linear relationship between the variables i.e. car price and car age. Additionally, the above argument would be supported with the fact that the maximum data points are fitting about a downward sloping line, which would result in low standard error and significant linear relationship of the variables. Part C - It is given in the question that the value of r2 = 0.894. Therefore, r2 = 0.894 r = = 0.945 (correlation coefficient) The value of the correlation coefficient may be positive or negative because the coefficient value is derived through taking the square root of coefficient of determination or R2. However, in the present scenario, negative slop (downward line) has obtained, which is evident in the scatter plot. Therefore, the value of r would be considered as -0.0945. Further, the r2 = 0.894 value would provide the evidence that approximately 89.4% of the deviation in the price of the cars would be explained or accounted for from the deviation in the age of the Toyota car. Part D In the present case, the given model would not account for 100% variability in the change of the price of the used Corolla cars because it is apparent from the data tables that for some of the sample vehicles, the prices are different even for the same age year. Thereby, it can be concluded that there are many factors (repairing, distance covered by car and so on) besides the age that tend to impact the vehicle price because the price and age are not providing r2=1. These imperative factors are essential in order to ascertain the price of the Corolla cars with higher precision. Part E It is mentioned in the given question that the regression line for the linear relationship model, is highlighted below: P = 12319.6 924 A Where, P = predicted price ($) A = age of car (year) There are two critical aspects in the given regression line Slope: The slope of the obtained regression line is computed as -924, which means that if the age of the used Corolla car is altered by one single year than the price of the car would be altered with the amount of $924, but in the opposite direction of the deviation in the car age. Y- intercept: The intercept of the regression line i.e. 12319.6 would provides that the price of the new Corolla car is the value of the intercept i.e. $12319.6. The price of 7 year old Corolla car would be calculated as A= 7 year, then price of car P = 12319.6 - 924 A P = 12319.6 (9247) = $5,851.6 It is recommended to the car purchaser to buy the vehicle (car), which comprises negative residual. Moreover, it is opined in the accordance of the regression line that negative residual indicates that the real price of the car is lesser in comparison of the possible expected price. This means that worth of the car is assumed to be much lower than the actual price and thus, the customer should buy the car. Beside this, the car with positive residual must not be bought because the car is overvalued and, thus not beneficial from the consumer perspective. Age of the car is given as 10 year old and the mentioned price is $1500. The aim is to compute the residual in the current case. Regression line P = 12319.6 - 924 A P = 12319.6 924 10 = $ 3,070.6 The price (predicted price) computed on the basis of the regression line is $3,070.6. Residual = Actual Price of the car - Predicted price of the car = 1500 - 3070.6 = -1,570.6 It is clear from the above calculations that negative residual has been obtained, which means the predicted value of the car is more than the actual price and thus, it is suggested to the concerned purchasers that the given car should be purchased. The aim is to find whether the current regression model is suitable to compute price for a 20 year old car. To find the usefulness/validity of this model, one needs to determine the price of a 20 year old car. Regression line P = 12319.6 - 924 A P = 12319.6 924 20 P = 12319.6 18,480 = -6,160.4 It is apparent from the above calculations that the price for 20 years old car comes out asnegative i.e. - 6,160.4, which is not possible and thus, this regression model would not be apply for evaluation of the price of 20 year old Corolla car.