Evaluating the Price of Premium Vehicles

Evaluating the Price of Premium Vehicles

Instructions/Descriptions

Evaluating the Price of Premium Vehicles

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Problem Description:

A local used car dealer in Berlin has asked us to evaluate the price of premium vehicles. We have collected data on 906 Mercedes listed on a used car website in 2016. They have provided us data on the price of the vehicle and characteristics of the vehicle such as age, kilometres driven, fuel used and the body style.

You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to complete this task.

Price (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: MonTuesWed.xlsx. You can find the data that we will use in the project in the “Processed” tab with the definitions of the variables in the “Dictionary” tab. For reference, we include the full dataset that can be found in the “Original” tab.

Required:

Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency (mean median and mode), variability (interquartile range, standard deviation) and shape (whether left or right skewed) for all the variables excluding Year, Name and Model. Include information regarding the quartiles for Price, Kilometres and PowerKW. How would you interpret the mean of dummy variables such as Automatic or Petrol? (1 Mark)

Draw a graph that displays the distribution of Price. Be sure to comment on the distribution. Does it appear normally distributed? (1 Mark)

Create a box-and-whisker plot for the distribution of Age and describe the shape. Is there evidence of outliers in the data? (1 Mark)

What is the probability that we could randomly select a vehicle that is a convertible? What is the likelihood that the age of a convertible exceeds 25 years? Is the age of a vehicle statistically independent of whether they are a convertible? Use a Contingency Table or Pivot Table to show the relative frequencies of these events. (2 Marks)

Estimate the 95% confidence interval for the population mean price of Hatchbacks. How does this compare to the 95% confidence interval for the population mean price of Coupes? (1 Mark)

It is traditionally believed that most hatchbacks in Germany have a manual transmission. Test the claim that the population proportion of Hatchback have a manual transmission exceeds 50% at the 5% level of significance. (1 Mark)

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Run a multiple linear regression using the data and show the output from Excel. Important: Exclude the dummy variable Coupe from the regression results as well as “Year” “name” and “model”. (1/2 Mark)

Is the coefficient estimate for Age statistically different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope. (2 Marks)

Evaluating the Price of Premium Vehicles

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