MATHEMATICS

Math's Assignment

Math's Assignment

Case Problem # 1: Variables Influencing the Price of Second-hand Car

Identification of Variable

The evaluation of the case problem is based on identifying and analyzing variables that are involved in the price shifts of second-hand car. The two variables identified for analyzing the influence of prices on second-hand car include Age/Years of the product and Mileage.

Methodology

Mileage

The first identified independent variable for the analysis is 'Mileage', which will be basis for collecting the data accordingly. The data collection process is done through simple random sampling and the foundation behind such collection is that the variable stands more independent. The dependant variable for the product is second-hand car price, which makes it viable to select a known market brand on which the analysis will be conducted. The brand in recognition for the analysis is Mazda for an open range of models of the brand. The sample size is twenty-five cars, which are checked for the mileage. The range of the Mileage sample starts from low to high, which is 148 miles to 99,000 miles.

Age/Years

The second independent variable for the analysis is 'Age/Years'. To incorporate such variable as the basis for the analysis, stratified sampling technique will be used for the data collection for the specified variable. The trademark in recognition for the data collection of the variable is Toyota and the brand is Yaris as the model. Similar to the above sample size, twenty-five samples have been collected or identified for the purpose of analysis. However, five samples are allocated to each of the year excluding the year zero. It has been stratified from the source of the website from where the data is observed that in every year has been put the lowest and the highest price in order to get a fair sample.

Evaluation of Graphical Data (Mileage)

Scatter Graph of Independent Variable Influencing Price of Second-hand Car

Analysis of Graphical Data (Mileage)

Regression Equation

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

Correlation

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

Regression & Correlation Relationship

Mileage - Influencing Price of Second-Hand Cars

The graphical representation of the observed variable in progression suggests that the correlation between the two dependent and the independent variable is negative. The analysis in this case reflects that the price of second-hand cars depend on mileage. The criterion is judge by considering the observed value in accordance with the ideal or benchmark value of negative correlation coefficient, which is -1. According to the result, the correlation is -0.72, as the current observed value is closer to the ideal value pointing a strong correlation. Such observation indicates correlation between mileage and price. Hence, the scatter graph shows that car with less mileage will have a higher resale price and vice versa.

Evaluation of Graphical Data (Age)

Scatter Graph of Independent Variable Influencing Price of Second-hand Car

Analysis of Graphical Data (Age)

Regression Equation

Price of second hand car influenced by Age: y = - ...