Georgia Votes 2000 ~ The 2000 presidential election between Al Gore and George W. Bush was the closest presidential election in the history of the United States. A social historian is investigating the relationship between race and voting results. For a random sample of 50 counties in the state of Georgia, the historian obtains the percentage of county residents who were African American (AA), and the percentage of ballots cast for Al Gore. Percentage AA is the X variable and Percentage vote for Al Gore is the Y variable in this scenario. Using the sample data, the historian finds the equation of the estimated regression line for predicting the Y variable to be yˆ = 25.4495 + 0.6956 x 44.0954% of Georgia's Baker county residents are African Americans. What is the estimated/predicted Percentage vote for Al Gore for this county? Give your answer to 4 decimal places. Note: Numbers are randomized for each instance of this question. Use the numbers given above.

The least square regression line is used to determine the relationship between a response variable (or dependent variable) and an explanatory variable (or independent variable).

The least square regression line can be used to predict the future value or estimate the past value of the dependent variable based on the independent variable.

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = response variable

x = explanatory variable

α = intercept

β = slope

The least square regression line for predicting the percentage vote for AI Gore (y) from the percentage of county residents who were African American (x) is given by:

[tex]\hat y=25.4495+0.6956 x[/tex]

Compute the predicted value of y for x = 44.0954% = 0.440954 as follows:

[tex]\hat y=25.4495+0.6956 x[/tex]

[tex]=25.4495+0.6956 \times 0.440954\\=25.4495+0.3067276024\\=25.7562276024\\\approx 25.76[/tex]

Thus, the predicted percentage vote for Al Gore for the county with 44.0954% African Americans is 25.76%.