# Welcome to Econ 420 Applied Regression Analysis Study Guide Week Nine.

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Welcome to Econ 420 Applied Regression Analysis Study Guide Week Nine

Some of you did not do as well as I expected on Assignment 2 So here is what we will do. 1.I explain the assignment. 2.You will redo Question 3 & 4 plus a couple of other questions. 3.You will utilize the discussion board of the WebCT to ask questions.

Assignment 7 Key (40 points) 1.#4, page 112 This regression has fallen into the dummy variable trap. CFP and NOCFP have a perfect linear relationship because CFP + NOCFP = 1 no matter what. This violates the assumption that two independent variables cannot have a perfectly linear relationship. The regression cannot be estimated. One of the two dummy variables, probably NOCFP, should be left out of the regression.

2. #5, page 112 a.Model ii is the best model. Model i has fallen into the dummy variable trap; one dummy variable must be omitted from the regression. Model iii does not have an intercept. b.Looking at model ii, the hypothesis that the seasons of the year don’t affect EMPLOYMENT would be H0: B2=B3=B4=0. Use an F-test to test this null hypothesis versus the alternative hypothesis that at least one of the seasons matter. For the test, Model ii is the unrestricted model. The restricted model is EMPLOYMENT = B0 + B1GDP + e.

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 Need to add an interaction variable to our equation: DVDEXP = B^ 0 + B^ 1 INCOME + B^ 2 PRICE + B^ 3 RAINFALL + 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^ 2 to 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)

To create the new variable “incomeXprice” in EViews: 1.Go to proc 2.Click on generate series 3.Enter the equation: inctimesprice= Income * Price Note: you can name the new variable whatever you would like. I have called it inctimesprice

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.

4, #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 10 9 or 5,280,000,000. The residual sum of squares for the unrestricted model is 4.33 x 10 9 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.

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). 5.92

Assignment 8 (40 points) Due: Before 10PM on Wednesday October 24 1.Redo Question 3 of Assignment 7 2.Redo Question 4 of Assignment 7 3.Question 10, Page 113 4.Question 12, Page 113

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