On the Internet, you can find information about prices of used cars. In the table below, we have listed the prices of used BMWs of the 3-series in Norway. We give the average price for a car that is 1, 2, 3, 4 and 5 years old.
The prices are given in thousands of euros.
(a) Build a linear model of the data.
(b) Graph the data and the linear model. Instead of a standard linear model, we assume that the price can be modeled as follows,
where we expect ˇ to be negative. By taking the logarithm of both side of (5.136), we get
This shows that we can compute ˛ and ˇ in (5.136) by constructing a linear model of the data given by
(c) Compute the entries of the following table:
(d) Compute a linear model
of the data in (c).
(e) Since
and define
(f) Plot the price-time data, the linear model and the exponential model. Which model seems to fit the data better?