A study used historical data to model the GOP per capita ot 24 countnes. One ana

Question

A study used historical data to model the GOP per capita ot 24 countnes. One analysis estimated the etet on GDP ot economic reguletions, using an index of the degree ot economic regulation and other vanables. They tound the regression madel in the accompanying table All t-statistics on the individual coefficients have P-values:0 05, except the coefficient of Primary Education Complete narts jand b) below Click the icon to viw the muliple regression model for GDP/Capita. a) lhe researchers hoped to show that more regilation leads to kwer Gl }P/Capita Dnes lhe coetticient ot the ronomic Regulatan Index demonstrate that') xplain Multiple Regression Madel for GDP/Capita A. O B ° C. D No, it says that the tect of more regulation on GDP is postive regardless or the other predictors in the model. Yes it says lhat U16 erecl ofrnure regulation on GDP s negative, tegardless oIhe ulher pred ctors in the rnodel. No, it says that after allowing for the effects of all the other predictors in the model, the effect of more regulation on ODP is negative Yes, it says lhal ane' allowing ru' lhe errects or all the olher predictors n the model the erect of rnoe iegulatiun cr' GDP spus live. GDP/ Capita= 10601-1304 Cuononic Regulation Index + 1.016 CDP Capita (10 years prior) 70.29 Ethno-linguistic Diversity Index 45.49 Trade as share of GDP-57 63 Primary Education 1% Cligible Population b The F-statistic for this model is 13221 5, 17 df). What do you conclude about the model? A. Theste tistic would yield p value that is not signific nt it cannot b. said with confidence that the regression coefficents ren't all zero. OB. The F-stetistic would yield a p-value that is signiticant It can be said with contidence that more regulation leads to lower GDPiCapita C. Ihe t statistic would yield a -value that s son ticant lt ran be said witn onnt dence that the regression r etc ents aren't all 7ero D The F statistic would yield a-aluc that s not significant it cannot be said with confidence that more regulation loads to lower GDP Capita Print Done c) It GI)PCapita 1) years pnor) is removed as a predictor, then the-statistc. arops to D(S1 and none ot the t-statstics are signitcant(aP-values2 Reconsider your interpretetion in parta O A. The interpretaton in part a is not valid Since Economic Rcgulation Index does not significantly contribute to this model, it is not reasonable to claim a relationship to GDP/Capita B. The coetticient of GDP, Caprta (10 years pnor) s actually a predictor at Economic Regulat on index C. The coefficient of the Economic Regulation lndex is ctually a predictor of GDP/Capria (10 years prior). OD. The interpretaton in part s is valid Allowing tor GOP Cepie (1 years prior, the other varisbles signficanty contnbute to the model; without allowing or GDP Cspita (10 years pnar), the other predictors do not

Explanation / Answer

As it is mentioned in the question, doinng parts a and b:

(a)

The multiple regression model for the GDP per capita has a negative coefficient for the economic regulation index in the presence of other predictor variables.

So, this means that after allowing for the effects of other predictors in the model, the effect of more regulation on GDP per capita is negative.

Thus, the coeffcient of economic regualtion in this model does not demonstrate that more economic regulation leads to lower DDP per capita.

Hence, the answer is = C

(b)

The F-statistic for this model is 132.21

The degrees of freedom for the F statistic is (5, 17)

So, the p-value is = P( F(5, 17) >= 132.21) = 5.467848e-13

This value is calculated using R as follows:

> 1 - pf(132.21, 5, 17)
[1] 5.467848e-13

Hence, the p-value for this model is staistically significant (as it is very very small.)

This means that we can reject the null-hypothesis and conclude that our model provides a better fit than the intercept-only model.

A significant overall F-test determines that the coefficients are jointly not all equal to zero.

Hence, the F-statistic yields a p-value that is significant: it can be said with confidence that the regression coefficient are not all zero.

Hence, the answer = C

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