MATHEMATICS

Assignment No. 3

Assignment No. 3

Problem No. 1: What influences the price of a second hand car?

Evaluation of the Data

The below mentioned scatter graphs shows two variables that include Mileage and Age of Years which influence the price of a second hand cars:

Methodology

Second Hand Car Price Influenced by Mileage

In order to collect the data for the variable that is mileage, simple random sampling has been conducted. The basis of using the simple random sampling is that the variable is more independent. Firstly, Mazda has been used as the brand, with any model on it. It used twenty five samples with the highest mileage is 99000 miles and lowest mileage is 148 miles.

Second Hand Car Price Influenced by Age

In context of the variable that is age; stratified sampling has been used in order to collect the data for this variable. It has been used because the author thinks this method is very suitable for this variable as a result of the year. First of all, to collect the data, the author chose Toyota as the brand and Yaris as the model. After that, 25 samples have been collected. Apart from 5 and 6 years, every year has been put 5 by samples. It has been stratified from the website sources that in every year has been put the lowest and the highest price in order to get a fair sample.

Evaluation of Graphs

Regression Equation on both Scatter Graphs of Factor that Influenced Price of Second Hand Car

Price of second hand car influenced by Mileage: y = - 40.837 x + 9258.4

Price of second hand car influenced by Age: y = - 1307.3 x + 11422

Calculation of Correlation from the Scatter Graph

Price of second hand car influenced by Mileage: R ² = 0.4927 and R = - 0.702

Price of second hand car influenced by Age: R ² = 0.7784 and R = - 0.882

Relationship of Correlation and Regression Equation with Price of Second Hand Car

Price of Second Hand Car Influenced by Mileage

From the graphical representation, it can be observed that there is negative correlation which reflects that the prices second hand cars depend on how far the car has been used for the journey, in other words the mileage. The ideal value of negative correlation coefficient is -1. Thus, the correlation coefficient in this case is -0.702 which shows that there is strong correlation of price of second hand care with its mileage; moreover, it can also be said that the mileage will affect the price of second hand car. Based on the scatter graphs with the correlation, it can be observed that the car with less miles shows the prices of the second hand cars will be higher.

Price of Second Hand Car Influenced by Age

From the above given graphical representation, it can be observed that there is strongly inverse correlation among the variables that are price and age of second hand cars. This shows that the second hand car prices are relatively depends on age, but ...