# Econ 420 by ert554898

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```									  Welcome to Econ 420
Applied Regression Analysis
Study Guide
Week Eight
Assignment 6 (20 points)

1.       Suppose the theory suggests that advertising for sun
blocks is more effective in summer than any other time
of the year
–     Formulate the model
•   Sales = B0 + B1 (Season) + B2 (Advertising) + error
–     What type of a data set will you use: time series or cross
sectional?
•   Time series
–     Set up a hypothesis to test the theory
–     The hypothesis of one sided t-test of significance on the
coefficient of Season is like:
•   H0: B1 ≤ 0
•   HA: B1 > 0
•   If we reject H0, then we have found significant evidence that
advertising for sun blocks is more effective in summer than any
other time of the year.
2. Suppose we estimate a regression equation that sets
the crime rate as a function of a state’s per capita
income and the number of police officers in each state
per 10,000 population. The estimated coefficient of per
capita income happens to be positive. We suspect that
the estimated coefficient of per capita income is biased
positively because we have an omitted variable. Which
of the following omitted variables is more likely to have
caused the bias in our estimated coefficient of income
and why?
–   Number of college educated individuals per 1000 population
–   Percentage of population living in poverty
–   State’s unemployment rate
–   Percentage of population who lives in urban areas.
•       Direction of bias in B percapita income = Bomitted * r included, omitted
•       Since B percapita income >0
•       Then there are two possibilities
•       (+) = (-) * (-), or
•       (+) = (+) * (+)
1.       Number of college educated individuals per 1000 population
can’t be it because it is positively correlated with percapita
income but it is expected to affect the crime rate negatively
–        Percentage of population living in poverty cant’ be it because
it is negatively correlated with percapita income but it is
expected to affect the crime rate positively.
–        State’s unemployment rate can’t be it because it is negatively
correlated with percapita income but it is expected to affect the
crime rate positively.
–        Percentage of population who lives in urban areas can be it
because it is positively correlated with percapita income and it
is expected to affect the crime rate positively.
Interaction Variables
• Suppose that the theory suggests that
advertising is more effective for new
products than for old products.
• Sales = Bo + B1 (adv) + B2 (adv * age) +
error
• Where (adv * age) is an interaction
variable
• Partial derivate of sales with respect to
– d sales /d adv = B1 + B2 * age
– Which mean that the advertising affects sales
depends on the age
– To find evidence for theory we should find that
B2 is negative
• How do we set up our hypotheses to test
the theory?
•   Y = Bo + B1 X1 + B2 X2 + B3 X3 + B4 X4 +
e
•   Ho: B2 = B4 = 0
•   HA: at least one is not zero
1. Estimate the model with X1 through X4 in
it (This is your unrestricted model.) find
2. Estimate the model with only X1 and X3
in it (This is you restricted model) find
• Which RSS you expect to be higher?
Why?
3. Find the critical F
–   Degrees of freedom for numerator = q = number of
restrictions
–   Degrees of freedom for denominator =n-k-1 (k is the
number of independent variables in the unrestricted
model)
divided by RSS unresrticted / n-k-1
5. If Fstat > F critical  reject Ho
Chow Test
•  Suppose you want to study the
relationship between hours of study and
grades and you have two samples
1. 100 MC students
2. 50 Washington State College
• You want to see if it is a good idea to
combine the two samples
Chow Test
• Estimate
• (1) GPA = Bo + B1 Study + B2 SAT + B3
Sleep +e    (for MC, sample n1 = 100)
• (2) GPA = Bo + B1 Study + B2 SAT + B3
Sleep +e    (for WS, sample n2 = 50)
• (3) GPA = Bo + B1 Study + B2 SAT + B3
Sleep +e    (for MC & WS, sample n1 + n2
= 150)
Hypotheses
• HO : There is no significant difference between
Bs from equation 1 and Bs from equation 2
• HA : Ho is not true
• Same F test as before
–   q = number of restrictions = 4 (k +1 in equation 1 or 2)
–   n- k-1 = n1 + n2 – 2 (k+1)= 150-8
Non-linear models
• The theory suggest that as Q (quantity of
out put) increases, TR (producer’s total
revenue) first goes up and then goes
down.
TR curve

20

16

TR
12
TR

8

4

0
0   1   2   3        4
fig      5   6   7
Quantity
• Would this equation capture the theoretical
shape of TR curve?
• TR = B0 + B1Q + error
• d TR/d Q = B1
• No, B1 can be either positive or negative
but not both.
• TR = B0 + B1Q2 + error
• d TR /d Q = 2B1Q
• No, Q is either 0 or positive. So,
depending on B1, the slope is either
positive or negative but not both
• TR = B0 + B1Q + B2 Q2 + e

• dTR/d Q = B1 + 2 B2 Q
• When Q is zero slope is B1
– So we expect B1 to be positive
• We expect B2 to be negative
– At high levels of Q, the negative component of the
slope (2B2Q) will greater that the positive component
of the slope (B1)
• How do you set up the null and alternative
hypotheses?
Double log Models
• Suppose your goal is to estimate the price
elasticity of demand (E)
• E =% change in Qd divided by % change in
Price
• ln Qd = B0 + B1 ln P + e
• d ln Qd / d ln P = B1= E
Semi Log Models
• Suppose you want to estimate the
percentage growth in a plant as a result of
1 more teaspoon of fertilizer
• ln Size= B0 + B1Fertilizer
• dlnSize/ d Fertilizer = B1
Assignment 7
(40 points)
Due: Before 10 PM on Friday October 19
1. #4, page 112
2. #5, page 112
3. Use the data set dvd4 and EViews to test
the hypothesis that at high levels of
income people are less sensitive to the
price of dvd than at low levels of income.
Use 5 percent level of significance.
#13, page 113

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