Based on annual data from 1990-2010, the following regressions were obtained: Mo

Question

Based on annual data from 1990-2010, the following regressions were obtained:

                  Model A: i = 2.69 – 0.48Xi                            R2 = .66

                                         (.122)   (.114)

                  Model B: ln(i) = 0.78 – 0.25ln(Xi)                R2 = .74

              (.0115)   (.049)

Where:

                  Yi = cups of coffee consumed by the ith person per day

                  Xi = price of a cup of coffee in dollars

                  ln( ) = natural log of ( )

                  *Standard errors are reported in parentheses

A. [6 points] How do we interpret the slope coefficients in the two models?

B. [8 points] Test the significance of the independent variable in each model using = .05.

C. [8 points] Construct a 95% confidence interval for the slope coefficient in each model. What is this measure telling us? How will consistency in your OLS estimation affect your confidence intervals?

D. [8 points] Since the R2 is larger in Model B compared to Model A, is this evidence that Model B is superior to Model A? Explain why or why not.

Explanation / Answer

A) 1= With an increase in the price of coffee by one unit there will be a reduction in the consumption of it by 0.48 unit.

2= With an increase in the price of coffee by one unit there will be ra eduction in the consumption of it by 0.25 unit.

B) Since p value of X1 is greater than alpha; (.114) > 0.05. we do not reject the null hypothesis.

In model 2, as “p < 0.05". Small p-values suggest that the null hypothesis is unlikely to be true. So we reject the null hypothesis.

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