Tutorial 7 27-01-10

Tutorial 7 27-01-10 - utorial T 7Workshop Wednesday27...

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Tutorial      7- Workshop      Wednesday 27     th     January, 2010     ECMT 1020 - Business and Economic Statistics B Aim: To alert students to potential data problems. Instructions: 1. Complete the "Learning the Concepts" questions BEFORE attending your workshop. (The questions will be reviewed in class) 2. The "Applying the Concepts" the questions will be done in workshop. 3. Complete the "Review Questions" after attending your workshop. These questions are in multiple choice format and are posted on blackboard. Learning the Concepts Question 1 (Multicollinearity) Regression output is supplied for two multiple regressions below. Which regression do you think is more likely to suffer from severe multicollinearity? Why? Regression One SUMMARY OUTPUT Regression Statistics R Square 0.98 Observations 100 Coefficient s Standard Error t Stat Intercept 5 0.5 10 x1 10 20 0.5 x2 8 20 0.4
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Regression Two SUMMARY OUTPUT Regression Statistics R Square 0.9 Observations 100 Coefficient s Standard Error t Stat Intercept 5 0.5 10 x1 10 5 2 x2 8 5 1.6 Question 2 (Dummy Variables) Using the following estimated model, ˆ 15 10 10 i i i y D x = + + where D = 1 if individual i is male; 0 otherwise Draw the separate male and female regression equations on the x-y plane. Applying the Concepts Question 3 Last week (Question Seven) we considered an international data set of country inflation rates. We constructed the multiple regression model: (7.1) y i = β 0 + β 1 x 1i + β 2 x 2i + ε ι where: y = inflation rate (%) x 1 = legal index of independence (1 - 10) x 2 = questionnaire index of operational independence (1 - 10) A question you were asked to consider was: were there any variables you considered omitted from the model? One key variable we might consider is whether a country is developed or not. (a) How would you incorporate a categorical variable such a whether a country is developed or not, into the regression model? (b) What sign would you expect on its coefficient? The following model was estimated: (7.1) Y i = β 0 + β 1 X 1i + β 2 X 2i + β 3 D i + ε ι
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where D i = 1 if a country is classified as developed, 0 otherwise. The estimated regression results are given below: Regression Statistics R Square 0.4316 Observations 22 ANOVA df SS MS F Significance F Regression 3 7347.624 2449.208 4.5568 0.0152 Residual 18 9674.739 537.4855 Total 21 17022.36 Coefficient s Standard Error t Stat P-value Intercept 60.7550 18.3957 3.3027 0.0040 LEGAL -0.1394 4.7868 -0.0291 0.9771 QUES -4.2035 3.2823 -1.2806 0.2166 DEV -23.5736 13.2568 -1.7782 0.0923 (c) Interpret the estimated dummy variable coefficient. Are the results as you expected? (d) Compare the results to the regression you estimated last week – is there evidence of omitted variable bias? (e)
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Tutorial 7 27-01-10 - utorial T 7Workshop Wednesday27...

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