Relationship between Price and Searching Time - Assignment Example

Assignment A1: Locate and select data Table 1: Used car listings from dealer websites S. No Make Model Km Driven Selling price ($) Dealer Name Green Star Rating (Stars) 1. Honda Accord 123,061 13,996 Adelaide City Honda 4 2. Subaru Forester 38,746 26,941 Adelaide City Subaru 3.5 3. Toyota Yaris 18,033 15,750 Melbourne City Toyota 5 4. Suzuki Swift 52,988 9,990 Sydney City Toyota - Source of listings in Table 1 S. No Source URL 1. http://www.carsales.com.au/dealer/details/Honda-Accord-2008/AGC-AD-16420520/?gts=AGC-AD-16420520>ssaleid=4470304 2. http://www.carsales.com.au/dealer/details/Subaru-Forester-2011/AGC-AD-16458969/?gts=AGC-AD-16458969>ssaleid=4470304 3. http://www.carsales.com.au/dealer/details/Toyota-Yaris-2013/AGC-AD-16339698/?Cr=1&sdmvc=1 4. http://sydneycitytoyota.com.au/used-cars/details/Suzuki/Swift/Rs415/2007/Hatchback/93442 Q1. A2: Data description Q2. The measurement properties for the different models of used cars on sale are as indicated in Table 2 below. These measurement properties include the number of kilometers driven, selling price ($) and the green star rating. Table 2: Descriptive statistics of the sampled car listings   Kilometers driven Selling price ($) Green star rating (Stars) Mean 58207 16669 4.2 Standard Error 22777.84 3629.88 0.44 Median 45867 14873 4 Mode #N/A #N/A #N/A Standard Deviation 45555.68 7259.76 0.76 Sample Variance 2075320025 52704171.58 0.58 Kurtosis 2.32 2.31 #N/A Skewness 1.41 1.33 0.94 Range 105028 16951 1.5 Minimum 18033 9990 3.5 Maximum 123061 26941 5 Sum 232828 66677 12.5 Count 4 4 3 As indicated in Table 2, the average kilometers driven for the four used car models was 58,207 kilometers, with a standard deviation of 45,555.68. Honda (Accord) is the model of the used car included in the sample listings with the highest number of kilometers driven (123, 061 km), while Toyota Yaris has the least number of kilometers driven (18,033 km). The average selling price for the sampled four used car models is $16,669, with a standard deviation of 7259.76. Subaru Forester is the most expensive used car model included in the sample car listings with a selling price of $26,941, while Suzuki Swift is the cheapest car model in the sample used car listings with a selling price of $9,990. The green star rating is a scale used to the rate the customers’ preference of the car model on sale. The maximum rating is a five star. For the sample of used car listings Toyota (Yaris) has the highest Green star rating of five stars. The green star rating for the Suzuki (Swift) was not provided in the dealer website. However, the average Green Star Rating for the three rated used car models is 4.2. A3: Data analysis Q3. Capecari’s consulting sample dataset Table 3: Descriptive statistics of Capecari’s consulting sample data   Total search time (hours) Price (AUD) Mean 35.01 14045.74 Standard Error 3.37 891.75 Median 23 13851.65 Mode 23 13851.65 Standard Deviation 33.51 8872.82 Sample Variance 1122.62 78726938.49 Kurtosis 2.68 2.50 Skewness 1.76 1.29 Range 147 50167.22 Minimum 1 0 Maximum 148 50167.22 Sum 3466.32 1390528.53 Count 99 99 Assuming that the Capecari’s consulting data set is normally distributed; the appropriate technique to identify any outliers that may be present in the data set is by determining values that are more or less than three standard deviations away from the mean. Lower limit =Mean-3(std.dev) Lower limit = 14045.74- 3(8872.82) -12572.72 No outliers present Upper limit = Mean - 3(std.dev) Upper limit = 14045.74 + 3(8872.82) 40664.2 There are outliers present There are price values included in the Capecari’s consulting data that are greater than the upper limit set for identifying the outliers present in the data set. This implies that the Capecari’s data set contains some outliers. To determine the number of outliers in the Capecari’s sample data set, identify the price values that are greater than $40,664.20. In the Capecari’s data set $50,167.22 is the only value that is greater than $40,644.20. Therefore, it can be concluded that Capecari’s data set has one value with a problem (outlier) assuming that the sample data set is normally distributed. As indicated in Table 3, the average selling price of used cars in the North American markets is $14,045.74, while the average selling price of the used cars in Australia included in the sample of used car listings in Table 1 is $16,669. Therefore, the average selling price of a used car in the Australian market is higher than that of a used car in the North American market. Q4. It is hypothesized that customers who search for high priced cars are likely to spend more time searching for used cars. To evaluate this hypothesis, a regression model used to estimate the time spent searching for used cars using the prices of the used cars, can be established. The linear regression model is as illustrated below; Time spent searching = β0 + β1 price The summary output of the regression analysis with the time spent searching (hrs) as the dependent variable and price (AUD$) as the independent variable is as follows; Figure 1 Substituting the estimated regression coefficients in the linear regression model, the equation of the derived regression model is as follows; Time spent searching = 22.43 + 0.000896 price As indicated the regression coefficient of price is 0.000896. This implies that there is a direct relationship between the price of a used car and the time spent searching for used cars. The regression coefficient of 0.000896 implies that a unit increase in price increases the time spent searching by 0.000896 hrs. The p-value of the regression is 0.018, which is less than the 0.05 level of significance. This further indicates that there is a statistically significant relationship between the price of used cars and the time spent searching for the used cars (Kutner, Nachtsheim & Neter, 2004). Q5. The correlation coefficient between the two variables is 0.24. This further indicates that there is positive direct relationship between price and searching time. Therefore, as the price of a car increases, the search time for the car also increases. In addition the coefficient of determination (R square) is 0.056, which implies that the price of a used car explains approximately 5.6% of the variability in the search time. As established there exists a statistically significant relationship between price and search time. Hence the price of a car can be used in to estimate the search time using the estimated regression model. However, based on the coefficient of determination, the percentage of variability in search time that is explained by the price of a car is 5.6% which is quite small. Therefore, to accurately estimate the search time, other information about consumer behaviour should be included in the model (Freedman, 2005). References Mogull, Robert G. (2004). Second-Semester Applied Statistics, Kendall/Hunt Publishing Company. Cook, A., Netuveli, G., & Sheikh, A. (2004). Basic Skills in Statistics: A Guide for Healthcare Professionals. London, GBR: Class Publishing. Groves, R. M., Fowler, F. J., Couper, M. P., Lepkowski, J. M., Singer, E., & Tourangeau, R. (2009). Survey Methodology. New Jersey: John Wiley & Sons. Freedman, A. D. (2005). Statistical Models: Theory and Practice, Cambridge University Press. Good, P. I., & Hardin, J. W. (2009). Common Errors in Statistics (And How to Avoid Them), (3rd ed.). Hoboken, New Jersey: Wiley. Kutner, M. H., Nachtsheim, C. J., & Neter, J. (2004). Applied Linear Regression Models, 4th ed., McGraw-Hill/Irwin, Boston. Read More