Part 3 Simple Linear Regression [20 marks]

The Toyota Hilux is the top selling car in Australia. The price of a previously owned Hilux depends on many factors, including the number kilometres (kms) travelled. To investigate the relationship between a cars kms and its sales price, data was collected on a sample of 20 used Hilux in Sydney.

The data for this question is provided here:

Questions (please answer them in excel if possible! :3)

a. [2 marks] Create a scatter plot for this data with kms as the independent variable. What does the scatter plot indicate about the relationship between price and kms?

b. [5 marks] Estimate a simple linear regression model with price as the dependent variable and kms as the independent variable. What is the estimated regression model (equation)?

c. [5 marks] Test whether each of the regression parameters (intercept and coefficient) is equal to zero at a 5% significance level. Interpret the coefficients of the estimated regression parameters and discuss whether these interpretations are reasonable.

d. [4 marks] Using the model estimated in part (b), calculate the predicted price for each of the cars in the sample. Based on the difference between the true and predicted prices, identify the two cars that were the biggest bargains. e. [4 marks] Suppose that you are considering purchasing a previously owned Hilux that has been driven 100,000 kms. Use the model estimated in part (b) to predict the price for this car. Is this the price you would offer the seller?

1 2 3 1 2 3 4 5 6 7 6 7 8 10 11 12 13 Price 69,700 66,900 61,900 61,000 59,000 49,000 54,800 42,800 46,900 45,000 43,000 45,900 35,500 34,600 34,900 31,900 36,500 28,000 27,000 19,000 Kms 13,400 21,100 15,900 62,000 43,000 80,000 41,200 152,000 130,000 120,000 94,000 111,900 135,000 167,000 142,300 220,000 122,000 206,500 226,000 275,000 14 15 16 17 18 19 20 1 2 3 1 2 3 4 5 6 7 6 7 8 10 11 12 13 Price 69,700 66,900 61,900 61,000 59,000 49,000 54,800 42,800 46,900 45,000 43,000 45,900 35,500 34,600 34,900 31,900 36,500 28,000 27,000 19,000 Kms 13,400 21,100 15,900 62,000 43,000 80,000 41,200 152,000 130,000 120,000 94,000 111,900 135,000 167,000 142,300 220,000 122,000 206,500 226,000 275,000 14 15 16 17 18 19 20