 Statistical Analysis
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# Statistical Analysis

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### Assessment details

• Assessment 1: Quiz
• Assessment 2: Project
• Assessment 3: Exam: closed book

### Solution

Relative XYZ,

ABC Location,

ABC State

Date: 21st January 2018

Dear Relative,

It has been a long time since our last visit. I hope you are doing well. As per your request, I determined whether there is a difference in average price between cars for sale privately and those for sale by a used car dealer. I used a sample of 121 cars where 40 cars consisted of sale privately, and 80 cars were sold by a used car dealer. I noted the price of both cars. The average price of the car being sold privately was found to be \$16,432.50 with deviation from the mean being \$7079.42.Further, the average price for a car sold by the dealer was found to be \$16,048.53 with deviation from the average price being \$6067.58. Based on the independent sample t-test, I found that there does not exist any significant difference between cars for sale privately and those sold by the dealer.

Also, you enquired about the depreciation in the price of the car. I used the same data set for this purpose using price as dependent variable and age as an independent variable. An initial analysis using Scatter plot between price and age of the car showed that price decreases with increase in age of the car(Figure 1 of Appendix).A negative relationship was found between price and age of the car, r=-0.8598.I further carried out regression analysis to confirm this. The variable, 'age' significantly predicted the car's price.I found that for a one year increase in age of the car, price decreases by \$1717.80(Table 2 of Appendix).Also, the price of the new car was found to be \$25133.60(Age=0).Further, 73.92% of the variation in the price of the car was found to be due to the age of the car (Table 2 of Appendix).

I further explored other independent factors that may have caused a depreciation in the price of the car. I considered using additional variables age and transmission type. The car transmission type consisted of automatic and manual. A multiple regression analysis was used for this purpose (Table 3 of Appendix). The percentage of variation in the price of the car explained by this model was found to be 80.26%.The multiple correlation coefficients for the multiple regression model was found to be 0.8959.All the variables showed depreciation in the price and were found to be significant. An increase in age by one year decreased the price of the car by \$1145.23, assuming odometer's reading to be the constant and automatic transmission. Also, a 1 km additional odometer reading decreased the price of the car by \$ 0.04, assuming age to be constant and transmission type to be automatic. Further, when age and odometer remained constant, the automatic car showed a decrease in price by \$1421.94.

Although, both simple and multiple regression models significantly predicted the price of the car based on the factors selected. However, the percentage of variation explained to predict price in case of multiple regression (r2=0.8026) was found to be greater than simple regression model (r2=0.7392). Thus, the best model to predict the price of the car would be based on factors such as age, transmission type, and odometer reading.

Regards

XXX