Question 1 (25 Marks)

You will use the data file usedcar.csv available on Moodle to answer this question. It is a dataset

of used cars listings from the UK and contains information on price, mileage, and registration year of

each used Toyota Yaris car on sale in 2020. Each observation is a car. The variables are as follows:

• price: listed price in British Pounds

• mileage: distance used (in 1000 miles)

• year: registration year

We are interested in the relationship between price (P) and mileage (M) of used Toyota Yaris

cars that were registered between 2010 and 2019 (inclusive). Using the data for cars with

registration years between 2010-2019, answer the following questions. Hint: Don’t forget to select

the relevant data first. See “Introduction to R” handout if you forget how to do this.

Page 1 of 2

(a) Generate the descriptive statistics for price, mileage and registration year and report them in

a table. (2 Marks)

(b) Plot price (y-axis) against mileage (x-axis). Label the axes clearly including the unit of each

variable, e.g. “Price (pounds)”. Do you observe any pattern? (3 Marks)

(c) Estimate the following linear regression model by least squares. Report the result in full (i.e.,

the fitted model, including s.e. and R-squared) and include your regression result from R in

your answer. (3 Marks)

Pi = ß1 + ß2Mi + ei (1)

(d) Interpret the estimated slope coefficient. Is this consistent with what you would expect the

relationship to be? Explain briefly. (3 Marks)

(e) Interpret the estimated intercept. Does it make sense? Comment. (3 Marks)

(f) Interpret the R2 you found in part (c). (1 Marks)

(g) Construct a 90% confidence interval for ß2 manually (i.e., write down the steps and perform

the calculation yourself rather than obtaining the confidence interval using R). Interpret the

confidence interval. (3 Marks)

(h) Predict price for a used Toyota Yaris that has travelled 20,000 miles. Show your calculation

and don’t forget to interpret your answer in words. (2 Marks)

(i) Test at the 1% level of significance if “an extra thousand mile of mileage is associated with a

decrease in the car price of OVER 90 pounds.” Be sure to show all the steps used to conduct

your test using the test statistics approach. Use R to find the exact t-critical value. (5 Marks)

# You will use the data file usedcar.csv available on Moodle to answer this question. It is a dataset of used cars listings from the UK and contains information on price, mileage, and registration year of each used Toyota Yaris car on sale in 2020

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You will use the data file usedcar.csv available on Moodle to answer this question. It is a dataset of used cars listings from the UK and contains information on price, mileage, and registration year of each used Toyota Yaris car on sale in 2020

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