Welcome to Econ 420 Applied Regression Analysis

1
Welcome to Econ 420 Applied Regression Analysis

• Study Guide
• Week Ten

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Ok People

• We have an Exam on Thursday, November 1.
• My original plan was to cover Chapter 6 before
  this exam. But I changed my mind. (Hope you
  dont mind.)
• So the Exam will cover only 2 chapters (4 5).
• We will cover Chapters 6, 7 and 8 after exam.
• I expect all of you to do extremely well on this
  exam.
• I am here to help. Use the Discussion Board to
  ask me questions.

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Assignment 8 Key (40 points)
4
1. 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

• Need to add an interaction variable to our
  equation
• DVDEXP B0 B1INCOME B2PRICE B3RAINFALL
  B4(inctimesprice)
• The interaction variable is inctimesprice which
  is INCOME PRICE
• Partial derivative (slope) of DVDEXP with respect
  to price is
• d(DVDEXP)/d (Price) B2 B4 Income
• You expect B2to be negative
• If the hypothesis is true then you also expect
  B4 to be positive (and smaller than B2)
• If B4 turns out to be significantly bigger than
  zero, then you have found evidence that at as
  income goes up the slope of DVDEXP with respect
  to PRICE goes down (becomes less of a negative)

5

• Step 1
• Null hypothesis H0 B4 0
• Alt. hypothesis HA B4 gt 0
• Step 2
• We will use 5 as our level of significance.
  Degrees of freedom n k 1 30 4 1 25
  tc 1.708 (from pg. 312). Decision rule reject
  null hypothesis if t gt tc, that is if t gt 1.708
• Step 3
• Run the regression
• The estimated coefficient on INCOMEXPRICE
  0.001973 and the t-stat 1.19
• Step 4
• Because our t-statistic, 1.19 is not greater than
  1.708, the null hypothesis B4 0 cannot be
  rejected at a 5 significance level we cannot
  say that at high levels of income people are less
  sensitive to the price of a dvd than those at low
  levels of income.

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2 13, page 113

• a. H0 B1B2, HA B1 is not equal to B2
• b. You will need to design your own F-test. The
  unrestricted model is
• CONSUMPTION B0 B1 INCOME B2 WEALTH e
• The restricted model is found by forcing the null
  hypothesis to be true. If B1B2 then
• CONSUMPTION B0 B1 INCOME B1 WEALTH e
• This is the same as
• CONSUMPTION B0 B1 (INCOME WEALTH) e
• where (INCOME WEALTH) is the only independent
  variable in the regression.
• Under EViews you will need to generate a new
  variable call it incwealth
• Incwealth INCOME WEALTH
• c. After estimating the restricted and
  unrestricted models, you should get a residual
  sum of squares for the restricted model of 5.28 x
  109 or 5,280,000,000. The residual sum of
  squares for the unrestricted model is 4.33 x 109
  or 4,330,000,000. q, the number of restrictions,
  is 1. B1 can take any value, and then B2 must
  take the same value as B1 for the null hypothesis
  to be true, so B2 has a restricted value if the
  null hypothesis is true. The null hypothesis
  used here only imposes one restriction.

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5.92

• The critical value for F1,27 with a 1 error
  level is 7.68. Since the calculated value of the
  F-statistic is lower than the critical value, we
  cannot reject the null hypothesis that B1B2.
  (Note that the critical value for a 5 error
  level is 4.21, so the null hypothesis could be
  rejected with a 5 error level).

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3 10, Page 113

• Regression Results for Professional Wrestling
  Model with an Interaction Variable
• Dependent Variable is HOURS
• Variable Coefficient Standard Error t-Statistic
• Constant 2.70 4.24 0.64
• MALE 4.73 1.76 2.69
• INCOME -0.00013 0.00013 1.06
• AGE 0.031 0.10 0.30
• AGExINCOME0.0000014 0.0000025 0.56
• Observations 20
• R2 0.47
• Adjusted R2 0.32
• Residual Sum of Squares 211.75
• F-statistic 3.26
• The slope estimate for AGExINCOME is
  statistically insignificant at any acceptable
  level of significance (up to 10). Meaning that
  the effect of income on hours of watching does
  not significantly depend on a persons age.
• Notes
• The presence of AGExINCOME causes the INCOME
  coefficient to become insignificant. (See Table
  5B, there is no interaction variable and the
  INCOME slope estimate is significant).
• The adjusted R2 of this estimation (0.32) is
  lower than the one in Table 5B (0.35), meaning
  that the interaction variable does not belong in
  the equation. In other words, It is an
  irrelevant variable.

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4 12, Page 113

• Need to use an F-test
• Unrestricted model is
• SALES B0 B1UNEMPLOY B2SUMMER B3FALL
  B4WINTER
• Restricted model is SALES B0 B1UNEMPLOY
• The hypotheses are
• H0 B2 B3 B4 0
• HA At least one of these Bs is not zero
• RSSrestricted 1,260,000,000
• RSS unrestircted 262,000,000
• N-k-1 17 and q3

10
The critical value of F3,17 at a 1 error level
is 5.19, so the null hypothesis is rejected.