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Econometrics – Practice Session #1
1. A researcher is analyzing data on the financial wealth of 100 professors at a small liberal
arts college. The values of their wealth range from $400 to $400,000, with a mean of
$40,000, and a median of $25,000. However, when entering these data into a statistics
software package, the researcher mistakenly enters $4,000,000 for the person with
$400,000 wealth. How much does this error affect the mean and median?
2. Which has a higher expected value and which has a higher standard deviation: a standard
six-sided die or a four-sided die with the numbers 1 through 4 printed on the sides?
Explain your reasoning, without doing any calculations, then verify, doing the
calculations.
3. Let us investigate the development of price of a product in a retail company. The price
depends on quantity of goods they sell plus the substituent price. The observations are
summarized in the following table:
Time
Product Price
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Quantity
21
23
25
26
25
21
28
29
23
26
27
32
32
34
38
40
38
Substituent Price
16
15
14
12
11
16
14
10
11
12
10
9
10
8
8
7
5
55
57
60
67
68
68
69
72
73
76
70
81
90
83
100
120
111
Using Excel or some mathematical software (e.g. Matlab) answer the following questions.
Remember to use matrix calculation (multiplication and inversion of the matrices, etc)
a) Using the Least Squares formula, estimate the coefficients b0, b1 and b2 and write the
model with quantified parameters.
b) Using your model, try to fit the values of product price.
c) Find and list the residuals of the model.
d) What is the sign of b1? What is the economic interpretation of that?
e) According to your model, does the relationship between product price and substituent
price exhibit constant, increasing or decreasing character? Explain.
f) How does the product price change if substituent price increases by one?
4. Even though model quantification via matrix calculation is successful in finding
parameters of OLS regression, it is not so effective (mainly due to a large number of
calculations). Knowing that, try to find another way how to get the values of parameters of
linear regression. (Hint: Excel is a powerful tool ).