Question

the population of lions in the wild has been decreasing according to a quadratic pattern. the scatterplot shows the relationship between the number of years since 1800, x, and lion population (in thousands), y. the equation for the least squares regression line shown is $hat{y}=35.5059 - 0.15094x$. what does the model predict to be the lion population in 2015 ($x = 215$)? a) 1.748 thousand lions b) 3.0538 thousand lions c) 7.215 thousand lions d) 9.326 thousand lions e) 13.114 thousand lions

Explanation:

Step1: Identify the regression - line equation

The regression - line equation is $\hat{y}=35.5059 - 0.15094x$.

Step2: Substitute the value of $x$

We are given $x = 215$. Substitute $x = 215$ into the equation:
$\hat{y}=35.5059-0.15094\times215$.
First, calculate $0.15094\times215 = 32.4521$.
Then, $\hat{y}=35.5059 - 32.4521$.
$\hat{y}=3.0538$.

Answer:

B. 3.0538 thousand lions