Question

Combining survey and voter turnout data, a regression plot is created with %turnout as the dependent variable, and the percentage of previous survey respondents who stated they had a high likelihood of voting as the independent variable (also as a percentage). The units of analysis are countries within the EU before a parliamentary vote.

Our best-fitting regression equation is as follows:

y=% predicted actual country voter turnout

x = % expected turnout from survey

y = -50.387% + 1.3789x

If the % expected turnout in a country is 70%, what would be the predicted actual turnout?

Next, the intercept is -50.387%. Although not seeming reasonable, interpret this intercept.

Then, y=% predicted actual country voter turnout

x = % expected turnout from survey

y = -50.387% + 1.3789x

Two countries differ in their survey expectation by 20%. Using this regression estimate, by what percentage would they be predicted to differ in their actual turnout and then find the value R-squared value for our equation is 0.4068. What does that value tell us about the relationship between expected and actual turnout?

Don't just write--"it's strong" or "moderate" or "weak." Make sure '40.68' or '.4068' appears somewhere in your answer.

Answer 1

Solution1:

given y=-50.387%+1.3789x

where

x=% expecetd turnout from survey

y=% predicted actual country voter turn out

Given x=70%

predicted actual turn out=

-50.387+1.3789*70

=46.136%

predicted ctual turn out=46.136

Solution2:

given y=-50.387%+1.3789x

where

x=% expecetd turnout from survey

y=% predicted actual country voter turn out

for y intercept put x=0

y=-50.387%+1.3789*0

y=-50.387%

that is when there are no % expected turnout from survey,

predicted actual country voter turn out decreases by 50.387%

y intercept ahs no meaning

Solution3:

r sq=0.4068

40.68% variance in  predicted actual country voter turn out is explained by expected turnout from survey

expalined variance=40.68%

unexplained variance=100-40.68=59.32%

rq=0.4068

r=sqrt(0.4068)=0.6378

there exists a strong positive relationship between y and x.