Suppose the population regression model, which shows the relationship between the explanatory variables (x1 and x2) and the dependent variable y, is given by log(y) = bo+! X1+b2x2+u Suppose the model has been estimated, and the results are as follows: log(y) = 5.1+2.6×1+0.9x2 Fill in the blanks below with the amount of rise in y and ŷ (y_hat) driven by causes provided in each sentence, respectively. From the coefficient estimate of b2, holding x1 constant, when x2 increases by 1 unit, y rises by %, which is an approximation that becomes more inaccurate as the change in log(y) increases. However, when x2 increases by one unit, y_hat rises by exactly %. When x2 decreases by one unit, y_hat falls by exactly %.

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Suppose the population regression model, which shows the relationship between the explanatory variables (x1 and x2) and the
dependent variable y, is given by
log(y) = bo +b1×1+b2x2+u
Suppose the model has been estimated, and the results are as follows:
log(y) = 5.1 +2.6x1+0.9x2
Fill in the blanks below with the amount of rise in y and ŷ (y_hat) driven by causes provided in each sentence, respectively.
From the coefficient estimate of b2, holding x1 constant, when x2 increases by 1 unit, y rises by
%, which is an approximation that becomes more inaccurate as the change in log(y) increases.
However, when x2 increases by one unit, y_hat rises by exactly
%. When x2 decreases by one
unit, y_hat falls by exactly
%.
Transcribed Image Text:Suppose the population regression model, which shows the relationship between the explanatory variables (x1 and x2) and the dependent variable y, is given by log(y) = bo +b1×1+b2x2+u Suppose the model has been estimated, and the results are as follows: log(y) = 5.1 +2.6x1+0.9x2 Fill in the blanks below with the amount of rise in y and ŷ (y_hat) driven by causes provided in each sentence, respectively. From the coefficient estimate of b2, holding x1 constant, when x2 increases by 1 unit, y rises by %, which is an approximation that becomes more inaccurate as the change in log(y) increases. However, when x2 increases by one unit, y_hat rises by exactly %. When x2 decreases by one unit, y_hat falls by exactly %.
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