Question

use the model to make the appropriate prediction.

a sociologist wanted to determine whether there was a relation between a states poverty rate (x) and its teen pregnancy rate (y). data from all 50 states produced the regression model:

\hat{y} = 4.3 + 1.4(x)

what does the model suggest for the teen pregnancy rate of florida, which has a poverty rate of 16.6?

\bigcirc 22.4%
\bigcirc 27.5%
\bigcirc 17%
\bigcirc 9.2%
\bigcirc 12.9%

Explanation:

Step1: Identify the regression model

The regression model is given by $\hat{y} = 4.3 + 1.4(x)$, where $x$ is the poverty rate and $\hat{y}$ is the predicted teen pregnancy rate.

Step2: Substitute the value of x

We are given that the poverty rate ($x$) for Florida is 16.6. Substitute $x = 16.6$ into the regression model:
$\hat{y} = 4.3 + 1.4\times(16.6)$

Step3: Calculate the value of $\hat{y}$

First, calculate $1.4\times16.6 = 23.24$. Then, add 4.3 to this result:
$\hat{y} = 4.3 + 23.24 = 27.54\approx27.5\%$

Answer:

27.5%