Question

Question 3 1 pts A political scientist was interested in studying America's voting habits. So, he decided to make a least squares regression equation to predict the percentage of people in a state that would vote for Obama in 2012 based on the percentage of people in a state that voted for Obama in 2008. The least squares equation is y-hat = -4.599 +1.04x. In the state of Alabama, 37.74% voted for Obama in 2008; whereas, 38.35% voted for him in 2012. What is the value of the residual? 0 -3.70 04.02 O 34.65 O 3.70 -4.02

Answer 1

ANSWER

GIVEN THAT

The least squares equation to predict the percentage of people at given will vote to obama in 2012 (y) based on the percentage of pepole in the state voted to Obama in 2008 (x) is given as:

$\hat{y}=-4.599+1.04x$

It is given that in state Florida, x=50.09 percent of pepole voted Obama in 2008; whereas y=50.01 percent voted Obama in 2012.

From the least-squares equation , the percentage of pepole at given state will vote Obama in 2012 is estimate as:

$\hat{y}$(%)=-4.599+1.04(50.09)

=47.4946

=47.49

Predicted value in 2012, $\hat{y}_{2012}$ =47.49%

Observed value in 2012, $y_{2012}$ =50.01%

Explation :

Substitute the value of X=50.09 into the regression equation the predicted value in 2012 is $\hat{y}_{2012}$ =47.49%

Then, compute the value of resident,

Residual =$y_{2012}$-$\hat{y}_{2012}$

=50.01-47.49

=2.52

Therefore, the value of residual is 2.52