presentation econometrics ex 1.pdf

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EX.1

The table below presents data from supermarket on monthly sales of apples ( A ,

in tones per month), average apples prices ( P A , in PLN/kg) and average

oranges prices ( P O , in PLN/kg) in the period August 2008 – January 2009.

t

A

P A

P O

1

6

1

7

2

6

2

6

3

4

3

6

4

3

4

5

5

2

5

4

6

3

5

3

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a)

What kind of relationship do You expect between the demand on apples

and the prices of apples and oranges?

When P A  then A ↑

When P A ↑ then A 

There is negative relationship between the prices of apples and demand on them.

When P O  then A 

When P O ↑ then A ↑

There is positive relationship between prices of oranges and demand on apples

b)

Estimate parameters of the model:

A = β 0 + β 1 *P A + β 2 P 0 + ε

Interpret the results.

6

PA

PO

1

1

7

6

1

2

6

Y =

4

X =

1

3

6

3

1

4

5

2

1

5

4

3

1

5

3

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Few steps to estimate parameters:

1. X T

2. X T X

3. det. (X T X)

4. (X T X) -1

5. X T Y

6. b=(X T X) -1 * X T Y

1.

X T =

1

1

1

1

1

1

1

2

3

4

5

5

7

6

6

5

4

3

X T X =

6

20

31

2.

20

80

92

31

92

171

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3. det. (X T X)  0

The result is 96 so it’s okay.

4.

(X T X) -1 = 54,3333

-5,9167

-6,6667

-5,9167

0,6771

0,7083

-6,6667

0,7083

0,8333

5.

X T Y =

24

67

134

6. b= (X T X) -1 * X T Y

b =

14,25

-1,71875

-0,875

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Plik z chomika:

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presentation econometrics ex 1.pdf (501 KB)

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