Question

Suppose that a regression line for some data transformed with logarithms predicts that when x equals 4, log(y) will equal 3.331. What does the regression line predict y will equal when x equals 4? Round your answer to the nearest whole number.
A. 101

B. 13

C. 3

D. 2143

Answer 1

Option D

The regression line predicts that at x = 4, y equals 2143

Solution:

Given that when x equals 4, log(y) will equal 3.331

To find: Find y when x equals 4

Since we have given that,

When x = 4,

$\text{ log } y = 3.331$

We need to find the value of 'y' when x = 4

$log_{10}y = 3.331$

Since it is logarithmic function with base 10, Raise to power of 10 on both sides,

$10^{log_{10}y} = 10^{3.331}\\\\\text{10 power log base 10 cancels, we get }\\\\y = 10^{3.331}\\\\y = 2142.89$

On rounding to nearest whole number, we get 2143

Thus Option D is correct