An economist investigated the association between a country\'s Literacy Rate and

Question

An economist investigated the association between a country's Literacy Rate and Gross Domestic Product (GDP) and used the association to draw the following conclusions. Explain why each statement is incorrect. (Assume that all the calculations were done properly.) a) The Literacy Rate determines 64% of the GDP for a country. b) The slope of the line shows that an increase of 5% in Literacy Rate will produce a $1 billion improvement in GDP. a) Choose the correct answer below. A. R^2 is an indication of the nonlinearity of the model. The model is 64% nonlinear for Literacy Rate. B. R^2 is the slope of the regression line. For each 1% in the Literacy Rate, the GDP increases by $640.00. C. R^2 is an indication of the appropriateness of the model. The model is 64% appropriate for Literacy Rate. D. R^2 measures the amount of variation explained by the model. Literacy Rate accounts for 64% of the Variability in GDP. b) Choose the correct answer below. A. Regression models can only be interpreted over specific intervals of the regression line. B. Regression models give averages, not predictions. The economist should have stated that the GDP will, on average, increase $1 billion if the Literacy Rate increases by 5%. C. Regression models give probabilities, not predictions. The economist should have stated that the GDP will most likely increase $1 billion if the Literacy Rate increases by 5%. D. Regression models cannot be interpreted causally. The modal says nothing about the actual consequence of changing the Literacy Rate.

Explanation / Answer

Answers

a. Option D

Explanation: The model adequacy is measured using the R2 value. Here R2 =64%. Thus 64% variability in the GDP can be explained by the regression model.

b. Option D

Explanation: The economist should have stated that the GDP will on average, increase $1 billion if the Literacy rate increases by 5%.

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