Question

The linearized regression equation for an exponential data set is log ŷ = 0.14x + 0.4, where x is the number of years and y is the population. What is the predicted population when x = 15?
A.3
B.126
C.316
D.9537

Answer 1

Explanation:

Here we know that the linearized regression equation for an exponential data set is:

$log \hat{y} = 0.14x + 0.4$

Where:

$\text{x: The number of years and} \\ \\ \text{y: The population}$

The predicted population when $x=5$ is found by substituting this value into the equation and finding $y$:

$log \hat{y} = 0.14x + 0.4 \\ \\ log \hat{y} = 0.14(15) + 0.4 \\ \\ log \hat{y} = 2.5 \\ \\ \hat{y}=10^{2.5} \\ \\ \hat{y} \approx 316.227$

Since population is a natural number, we must round off, therefore, the predicted population is 316, option C.