ECOM30001 Lecture Notes - Lecture 10: Scatter Plot, Statistical Hypothesis Testing, Bias Of An Estimator

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orchidgnu53

27 Jul 2018

School

University of Melbourne

Department

Econometrics

Course

ECOM30001

Professor

Andrew Clark

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Document Summary

Heteroskedasticity exists when the variance of the random error is not the same for all observations. If scatter of y around the mean increases/decreases as x increases, then the uncertainty about y changes as x changes suggests variance is not constant. If we have a linear regression model that satisfies all assumptions except (cid:1844)(cid:4666)(cid:3036)(cid:4667)=(cid:3036)(cid:2870) then: Ols estimator (cid:1854)(cid:3037) is still unbiased under heteroskedasticity: (cid:1831)[(cid:3036)|(cid:3036)]=(cid:882, however, (cid:1844)(cid:4666)(cid:1854)(cid:3037)(cid:4667) derived under assumption of homoskedasticity will no longer be correct. Squared residuals are used to approximate the variance of the known random errors: the x"s are fixed in repeated sampling. Note: overall f-statistic computed by r is no longer correct need to compute using variance-covariance matrix. One with a lower variance than white"s covariance matrix. When heteroskedasticity exists we can make an assumption about the unknown error variance in order to transform them into homoscedastic errors. R & d e x a m p l e. For the original model the following assumptions hold:

Related Questions

TABLE 66 Stock Prices and Consumer Prices

CITY
Y = Rate of Change, Stock Prices, Percent Per Year
X = Rate of Change, Consumer Prices, Percent Per Year

CITY	Y	X
A	5	4.3
B	11.1	4.6
C	3.2	2.4
D	7.9	2.4
E	25.5	26.4
F	3.8	4.2
G	11.1	5.5
H	9.9	4.7
I	3.3	2.2
J	1.5	4
K	6.4	4
L	8.9	8.4
M	8.1	3.3
N	13.5	4.7
O	4.7	5.2
P	7.5	3.6
Q	4.73.	6
R	8	4
S	7.5	3.9
T	9	2.1

Table 66 gives data on percent change per year stock prices (Y) and consumer prices (X) for a cross section of 20 cities.

******************* answer in "SAS format" please********************* (if possible)

1) Plot the data in scattergram

2) Regress Y on X and examine the residuals from this regression. What do you observe?

3) Since the data for city(E) is unusual, repeat the regression in (2) dropping the data on city(E). Now examine the residuals from this regression. What do you observe?

4) If on the basis of the results in (2) you conclude that there was heteroscedasticity in the error variance but on the basis of the results in (3) you reverse your conclusion, what general conclusions do you draw?

State whether the following statements are true or false. Breifly justify your answer:

5) When autocorrelation is present, OLS estimators are biased as well as inefficient;

6) The R squared values of two models, one involving regression in the first-difference form and another in the level form, are not directly comparable.

7) In the presence of heterscedasticity the usual OLS method always overestimates the standard errors of estimators.

8) If a regression model is mis-specified (e.g., an important variable is ommitted), the OLS residuals will show a distinct pattern.

redcamel374

1.Write a function encipher(s, n) that takes as inputs an arbitrary string s and a non-negative integer n between 0 and 25, and that returns a new string in which the letters in s have been "rotated" by n characters forward in the alphabet, wrapping around as needed. For example:

>>> encipher('hello', 1) result: 'ifmmp'

>>> encipher('hello', 2) result: 'jgnnq'

>>> encipher('hello', 4) result: 'lipps'

Upper-case letters should be "rotated" to upper-case letters, even if you need to wrap around. For example:

>>> encipher('XYZ', 3)

result: 'ABC'

Lower-case letters should be "rotated" to lower-case letters:

>>> encipher('xyz', 3)

result: 'abc'

Non-alphabetic characters should be left unchanged:

>>> encipher('#caesar!', 2)

result: '#ecguct!'

Hints/reminders:

You can use the built-in functions ord and chr convert from single-character strings to integers and back:

>>> ord('a')

result: 97

>>> chr(97)

result: 'a'

You can use the following test to determine if a character is between 'a' and 'z' in the alphabet:

if 'a' <= c <= 'z':

A similar test will work for upper-case letters.

We recommend writing a helper function rot(c, n) that rotates a single character c forward by n spots in the alphabet. We have given you a template for this helper function in ps3pr3.py that checks to ensure that c is a single-character string. We wrote rot13(c) in lecture; rot(c, n) will be very close to rot13(c)! You can test your rot(c, n) as follows:

>>> rot('a', 1)

result: 'b'

>>> rot('y', 2)

result: 'a'

>>> rot('A', 3)

result: 'D'

>>> rot('Y', 3)

result: 'B'

>>> rot('!', 4)

result: '!'

Once you have rot(c, n), you can write a recursive encipher function.

Once you think you have everything working, here are three more examples to try:

>>> encipher('xyza', 1)

result: 'yzab'

>>> encipher('Z A', 2)

result: 'B C'

>>> encipher('Caesar cipher? I prefer Caesar salad.', 25)

result: 'Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.'

2.Write a function decipher(s) that takes as input an arbitrary string s that has already been enciphered by having its characters "rotated" by some amount (possibly 0). decipher should return, to the best of its ability, the original English string, which will be some rotation (possibly 0) of the input string s. For example:

>>> decipher('Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.')

result: 'Caesar cipher? I prefer Caesar salad.'

Here are two more examples:

>>> decipher('Hu lkbjhapvu pz doha ylthpuz hmaly dl mvynla lclyfaopun dl ohcl slhyulk.')

result: 'An education is what remains after we forget everything we have learned.'

>>> decipher('python')

result: 'eniwdc'

------------------------------------

def rot(c, n):
""" your docstring goes here """
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

def letter_prob(c):
""" if c is the space character (' ') or an alphabetic character,
returns c's monogram probability (for English);
returns 1.0 for any other character.
adapted from:

"""
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

if c == ' ': return 0.1904
if c == 'e' or c == 'E': return 0.1017
if c == 't' or c == 'T': return 0.0737
if c == 'a' or c == 'A': return 0.0661
if c == 'o' or c == 'O': return 0.0610
if c == 'i' or c == 'I': return 0.0562
if c == 'n' or c == 'N': return 0.0557
if c == 'h' or c == 'H': return 0.0542
if c == 's' or c == 'S': return 0.0508
if c == 'r' or c == 'R': return 0.0458
if c == 'd' or c == 'D': return 0.0369
if c == 'l' or c == 'L': return 0.0325
if c == 'u' or c == 'U': return 0.0228
if c == 'm' or c == 'M': return 0.0205
if c == 'c' or c == 'C': return 0.0192
if c == 'w' or c == 'W': return 0.0190
if c == 'f' or c == 'F': return 0.0175
if c == 'y' or c == 'Y': return 0.0165
if c == 'g' or c == 'G': return 0.0161
if c == 'p' or c == 'P': return 0.0131
if c == 'b' or c == 'B': return 0.0115
if c == 'v' or c == 'V': return 0.0088
if c == 'k' or c == 'K': return 0.0066
if c == 'x' or c == 'X': return 0.0014
if c == 'j' or c == 'J': return 0.0008
if c == 'q' or c == 'Q': return 0.0008
if c == 'z' or c == 'Z': return 0.0005
return 1.0

olivemink636

Match the definitions or complete the statements in the first part of the quiz with the appropriate terms found in the second part.

Definitions/Statements

1. _____ refers to marketersâ focus on a product rather than on the needs of the market.

2. _____ companies do not try to persuade consumers to buy what the firm has already produced, but rather to produce only products that they know they can sell, thereby satisfying consumersâ needs and turning them into loyal customers.

3. The impact of technology on buyer behavior relates to factors such as ____; the use of technology to engage customers and build relationships; customization of products and promotional messages; and better prices and distribution.

4. In the case of situational influences, this relates to the situation in which or the occasion on which the product will be used, e.g., special occasion or everyday use.

5. In the case of situational influences, this relates to the fact if we are in a store, point-of-purchase displays could influence us to buy something. We could also make unplanned purchases because we remembered something from seeing the brand while we are in the store.

6. This discipline on which consumer researchers draw focuses on society and large groups in society such as family and social class.

7. This discipline on which consumer researchers draw focuses on cultures and differences among cultures.

8. These are temporary circumstances that affect consumer purchase decisions.

9. In the case of situational influences, this refers to the fact that the person and the occasion for which we are buying something influence our purchase decisions.

10. According to the simple model of consumer decision making, reference groups, family, social class, culture, and subculture are among the _____ on buyer behavior.

11. According to the simple model of consumer decision making, motivation, personality trait, perception, and attitudes are among the _____ on buyer behavior.

12. According to the simple model of consumer decision making, advertising, buzz agents, customized messages, social media, and word-of-mouth are examples of ____.

13. This discipline on which consumer researchers draw focuses on behavior in small groups and helps consumer researchers to understand issues such as opinion leadership, diffusion of innovations, and communication.

14. In the case of situational influences, ______ are consumer mood states or physiological state (for example, hunger, thirst) that influence consumer decision-making.

15. The selection of one or more segments by a marketer to serve.

16. Developing a distinct image for a brand in the mind of consumers.

17. This is an effort by a marketer to change the existing perception that consumers have of a brand.

19. ___ segmentation involves segmenting based on variables such as urban, rural, suburb, state, cities, counties, and regions.

20. ____ segmentation is based on variables such as consumersâ lifestyles as indicated by their activities, interests, and opinions.

21. This criterion for effective targeting says that marketers should have some way of deciding which consumers fall into which segments.

22. This criterion for effective targeting says that marketers should be able to reach segments with appropriate media and distribution channels.

23. This is the most popular segmentation system combining lifestyles and values of consumers.

24. This household segmentation model is based on a combination of geographic and demographic information and the principle that âBirds of a feather flock together.â

25. ______ is defined as âsending consumers personalized and prompt offers and promotional messages designed to reach the right consumers and deliver to them highly relevant messages at the right time and more accurately than when using conventional segmentation techniques.â

Terms

A. Positioning

B. Accessibility

C. Anthropology

D. Situational influences

E. Consumption situation

F. Task definition

G. Identification

H. Marketing-oriented

I. Targeting

J. Psychographic

K. Marketing myopia

L. PRIZM

M. Interactive and novel communication channels

N. Sociology

O. Demographic

P. Purchase situation

Q. Behavioral targeting

R. Antecedent states

S. Communication sources

T. Geographic

U. Sociocultural influences

V. VALS

W. Psychological influences

X. Social psychology

Y. Repositioning

ECOM30001 Lecture Notes - Lecture 10: Scatter Plot, Statistical Hypothesis Testing, Bias Of An Estimator

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