Welcome to Econ 420 Applied Regression Analysis

1. Welcome to Econ 420 Applied Regression Analysis Study Guide Week Ten

2. 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 don’t 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.

3. 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 = B^0 + B^1INCOME + B^2PRICE + B^3RAINFALL + B^4(inctimesprice) • The interaction variable is inctimesprice which is INCOME * PRICE • Partial derivative (slope) of DVDEXP with respect to price is • d(DVDEXP)/d (Price) = B^2 + B^4 Income • You expect B^2to be negative • If the hypothesis is true then you also expect B^4 to be positive (and smaller than B^2) • If B^4 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 > 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 > tc, that is if t > 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.

6. 2: #13, page 113 a. H0: B1=B2, 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 B1=B2 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.

7. 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 B1=B2. (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).

8. 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 person’s 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.

9. 4: #12, Page 113 • Need to use an F-test • Unrestricted model is • SALES^ = B^0 + B^1UNEMPLOY + B^2SUMMER + B^3FALL + B^4WINTER • Restricted model is SALES^ = B^0 + B^1UNEMPLOY • The hypotheses are • H0: B2 = B3 = B4 = 0 • HA: At least one of these B’s is not zero • RSSrestricted = 1,260,000,000 • RSS unrestircted = 262,000,000 • N-k-1 =17 and q=3

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