Repeat problem 1 for the regression of problem 3.
Problem 1
Produce residual plots for the regression of problem 2. Is there any apparent model inadequacy?
Problem 2
An article in the Journal of Monetary Economics assesses the relationship between percentage growth in wealth over a decade and a half of savings for baby boomers of age 40 to 55 with these people's income quartiles. The article presents a table showing five income quartiles, and for each quartile there is a reported percentage growth in wealth. The data are as follows.
|
Income quartile:
|
1
|
2
|
3
|
4
|
5
|
|
Wealth growth (%):
|
17.3
|
23.6
|
40.2
|
45.8
|
56.8
|
Run a simple linear regression of these five pairs of numbers and estimate a linear relationship between income and percentage growth in wealth.
Problem 3
An article in Worth discusses the immense success of one of the world's most prestigious cars, the Aston Martin Vanquish. This car is expected to keep its value as it ages. Although this model is new, the article reports resale values of earlier Aston Martin models over various decades.
|
Decade:
|
1960s
|
1970s
|
1980s
|
1990s
|
2000s
|
|
Present value of Aston Martin Model (average)
|
$180,000
|
$40,000
|
$60,000
|
$160,000
|
$200,000
|
Based on these limited data, is there a relationship between age and average price of an Aston Martin? What are the limitations of this analysis? Can you think of some hidden variables that could affect what you are seeing in the data?