# The proportion of voters who voted for democratic

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read and understand the table. The proportion of voters who voted for Democratic Senator candidate Nelson and Ref candidate Buchanan on election day was 0.0102. In comparison, the proportion of voters who cast a ballot who voted for Nelson and Buchanan by absentee ballot was a mere 0.0017, 6 times less than the election proportion. The authors attribute the butterfly ballot to the huge difference in voter proportion between absentee and election-day ballots. *** ### Question 4. Helping out your FRIENDS You mentioned to your friend that you're learning some really neat stuff in PS 15. Now they're curious. They want to know how they too can figure out relationships in the political world. ####(a) Your friend asks how correlation is different from covariance, and for a formula that can turn $cov(x,y)$ into $cor(x,y)$. Provide that formula, and explain how correlation relates to covariance. Also explain what the correlation means and the possible values it can take. Correlation: $$cor(x,y) = \frac{cov(x,y)}{(SD(x)*(SD(Y))}$$ Correlation is a scaled version of Covariance. It measures the strength of the relationship between the independent and dependent variables (x & y) between the values of 1 to -1; changes in scale don't affect the value. A positive value means that the x & y variables are positive correlated. A negative value means that the x & y values are negatively correlated. A 0 means that there is no correlation. Covariance: $$cov(x,y) = \frac{\sum_{i=1}^n(X_i-X)(Y_i - Y)}{n-1}$$ Covariance is a measure of correlation; it measures the extent that the independent variable and dependent variable (x & y) change together; thus, it is affected by a change in scale. ####(b) Your friend asks you to explain what a random variable is--in your own words, provide a definition. What are its key components? A random variable is a variable that has a range of different potential values, each with a probability of being chosen. The probabilities have a set distribution that can be graphed as a curve.

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####(c) Your friend then says they have heard of linear regression before, but they don't know how it works. Explain in simple language what the regression is doing to estimate a relationship between two variables. Come up with a specific political science example to help your friend understand. Linear regression estimates the relationship between an independent variable (the cause or reason for an outcome) and a dependent variable (the outcome). An example of a linear regression in politics is the relationship between income bracket (independent variable) and how that affects political affiliation (dependent variable).
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