A study used historical data to model the GDP per capita of 24 countries. One an
ID: 3338007 • Letter: A
Question
A study used historical data to model the GDP per capita of 24 countries. One analysis estimated the effect on GDP of economic regulations, using an index of the degree of economic regulation and other variables. They found the regression model in the accompanying table. All t-statistics on the individual coefficients have P-values 0.05, except the coefficient of Primary Education. Complete parts a) and b) below. Click the icon to view the multiple regression model for GDP/Capita. a) The researchers hoped to show that more regulation leads to lower GDP/Capita. Does the coefficient of the Economic Regulation Index demonstrate that? Explain Xi 0 A Yes, it says that the effect of more regulation on GDP is negative, regardless of the other predictors in the model. O B. No, it says that affer allowing for the effects of all the other predictors in the model, the effect of more regulation on GDP is negative O C. No, it says that the effect of more regulation on GDP is postive, regardless of the other predictors in the model. O D. Yes, it says that after allowing for the effects of all the other predictors in the model, the effect of more regulation on GDP is positive. Multiple Regression Model for GDP/Capita GDP/Capita-10075-1343 Economic Regulation Index+1.035 GDP Capita (10 years prior)-71.78 Ethno-linguistic Diversity Index+43.32 Trade as share of GDP-5888 Primary Education (% Eligible Population) b) The F-statistic for this model is 128.01 (5, 17 df). What do you conclude about the model? O A. The F-statistic would yield a p-value that is significant. It can be said with confidence that more regulation leads to lower GDP/Capita. O B. The F-statistic would yield a p-value that is not significant. It cannot be said with confidence that the regression coefficients aren't all zero. ° C. The F-statistic would yield a p value that is not 9ignificant. It cannot be said with confidence that more regulation leads to lower GDP/Capita D. The F-statistic would yield a p value that is significant it can be said with confidence that the regression coefficients arent alzer Print Done c) f GDP/Capita (10 years prior) is removed as a predictor, then the F-statistic drops to 0.711 and none of the t-statistics are significant (all P- 0.22). Reconsider your interpretation in part a. OA. The interpretation in part a is not valid. Since Economic Regulation Index does not significantly contribute to this model, it is not reasonable to claim a relationship to GDP/Capita. 0 B. The coefficient of the Economic Regulation index is actually a predictor of GDP / Capita (10 years prior). ° C. The coefficient of GDP / Capita (10 years prior) is actually a predictor of Economic Regulation Index. D. The interpretation in part a is valid. Allowing or GDP/ Capita 10 years prior the ot er vanables significantly contribute to the model; without allowing or GDP/ Capita 10 years prior the other predictors do notExplanation / Answer
Answer to the question is as follows:
a. A is right. The coefficient' effect on the dependent variable ( GDP/capita) is irrespective of other variables
b. With a 128.01(5,17) , the p-value' less than .00, and hence, the Fstatistic is significant.
The Fstatistic is for the linear regression equation and not for individual variable. Hence, D is the right interpretation of the result.
c. If none of t-statistics is significant, then the even part a) is insignificant.
A is right in this case. Interpretation in parta. doesn't hold true any longer. Since this variable doesn't contribute to this model, it isn't reasonable to claim a relationship to GDP/Capita
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