Question

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 Florida, 50.09% voted for Obama in 2008; whereas, 50.01% voted for him in 2012. What is the value of the residual? Group of answer choices

Answer 1

Answer:

The value of residual is 2.5131%.

Step-by-step explanation:

We are given the following in the question:

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

The above is a linear 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.

Independent Variable:

Percentage of people in a state that voted for Obama in 2008

Dependent Variable:

Percentage of people in a state that would vote for Obama in 2012

In the state of Florida, 50.09% voted for Obama in 2008; whereas, 50.01% voted for him in 2012.

Thus, the actual value is 50.01%.

We predict the value from regression equation by putting x = 50.09

$\hat{y}= -4.599 +1.04(50.09) = 47.4946$

The predicted value for percentage of people in a state that would vote for Obama in 2012 is 47.4969%.

Residual is the difference between the predicted value and the actual value.

$\text{Residual} = \text{Observed - Predicted}\\= y-\hat{y}\\= 50.01\% - 47.4969\%\\= 2.5131\%$

Thus, the value of residual is 2.5131%.