Suppose that a regression line for some data transformed with logarithms predicts that when x equals 9, log(ŷ) will equal 3.992. What does the regression line predict ŷ will equal when x equals 9?

Question

Suppose that a regression line for some data transformed with logarithms predicts that when x equals 9, log(ŷ) will equal 3.992. What does the regression line predict ŷ will equal when x equals 9?

Answer 1

To find the predicted value ŷ when x equals 9, we need to reverse the logarithmic transformation. We know that the logarithm of ŷ is 3.992 when x equals 9, so we can use the exponentiation property of logarithms:

ŷ = 10^(log(ŷ)) = 10^3.992

Using a calculator, we can find that 10^3.992 ≈ 1346.23. Therefore, the regression line predicts that ŷ will equal approximately 1346.23 when x equals 9.