Assume the following table lists campaign spending, in thousands of dollars, by candidates for statewide office and the percentage of the popular vote they received in their respective districts: Spending 11.5 51.1 17.9 4.9 12.9 20.5 76.4 Percentage 33.4 12.8 61.2 50.2 78.1 14.1 49.9 Does a strong linear correlation exist between campaign spending and percentage of votes received? How do you know? If a strong linear correlation exists, answer the following: a.) Find a regression model (ax+b) for percentage of votes received as a function of campaign spending. b.) If a politician spent $60,000 on a campaign, what percentage of the vote should she expect to receive? Also, is this interpolation or extrapolation? Why? c.) If a politician received a quarter of the votes, what would you expect the campaign to have spent?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Assume the following table lists campaign spending, in thousands of dollars, by candidates for statewide office and the percentage of the popular vote they received in their respective districts:
Spending
11.5
51.1
17.9
4.9
12.9
20.5
76.4
Percentage
33.4
12.8
61.2
50.2
78.1
14.1
49.9
Does a strong
If a strong linear correlation exists, answer the following:
a.) Find a regression model (ax+b) for percentage of votes received as a
b.) If a politician spent $60,000 on a campaign, what percentage of the vote should she expect to receive? Also, is this interpolation or extrapolation? Why?
c.) If a politician received a quarter of the votes, what would you expect the campaign to have spent?
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