Problem Description:
A resale market for automobiles would like to know what features of automobiles are typically driving the prices of new vehicles. This is especially important in helping to design their website in order to highlight the critical features that consumers are concerned with. A sample of 35 recent models of automobiles was taken. Several characteristics of the automobiles including the power of the engine, weight, fuel efficiency, type of transmission as well as the body style were included in the table.
You will use descriptive statistics, inferential statisticsand your knowledge of multiple linear regression to complete this task.
Price (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: Wednesday.xlsx.
Here is a table describing the variables in the data set:
|
Variable
|
Definition
|
|
Price
|
Drive-away price of vehicle including taxes and fees
|
|
Power
|
Power of engine in kW
|
|
Kerb Weight
|
Mass of vehicle in kg with standard equipment and unoccupied
|
|
Fuel
|
Typical fuel usage in Litres per 100 km
|
|
Automatic
|
Dummy variable to indicate that the vehicle has an automatic transmission
|
|
Hatchback
|
Dummy variable to indicate that the body type is a hatchback
|
|
Sedan
|
Dummy variable to indicate that the body type is a sedan
|
|
SUV
|
Dummy variable to indicate that the body type is a SUV
|
|
Convertible
|
Dummy variable to indicate that the body type is a convertible
|
Required:
A. Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency,variability and shape for Price, Power, Kerb Weight and Fuel. How would you interpret the mean of dummy variables such as Automatic or Hatchback?
B. Draw a graph that displays the distribution of fuel consumption. Be sure to comment on the distribution.
C. Create a box-and-whisker plot for the distribution of the prices and describe the shape. Is there evidence of outliers in the data?
D. There is a common belief that hatchbacks are underpowered. What is the likelihood that a hatchback will has an engine that has more than 100 kW power? Is the engine power statistically independent of the type of vehicle body? Use a Contingency Table.
E. Estimate the 95% confidence interval for the population mean kerb weight.
F. The Department of Infrastructure and Regional Development has recently stated that they would like to see SUVs become more fuel efficient, specifically under 9 L per 100 km. Test the claim at the 10% level of significance that the fuel efficiency is below 9 L per 100 km.
G. Run a multiple linear regression using the data and show the output from Excel. Exclude the dummy variable "Convertible" from the regression results.
H. Is the coefficient estimate for the Power 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.
I. Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning.
J. Interpret the value of the Adjusted R2. Is there a large difference between the R2 and the Adjusted R2? If so, what may explain the reasoning for this?
K. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.
L. Based on the results of the regressions, what other factors would have influenced the price of vehicles? Provide a couple possible examples and indicate their predicted relationship with the review score if they were included.
M. Predict the average price of a hatchback which weighs 1100 kg with 97 kW of power that uses 6.7 L per 100 km of fuel if it is appropriate to do so. Show the predicted regression equation.
N. Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots and/or histograms and Explain.
O. Would these results tell us anything about the population distribution of vehicles on the road? If not, describe a scenario in how you would construct a sample to sample vehicles on the road.
Attachment:- business-statistics.xlsx