The following model can be used to study whether campaign expenditures affect election outcomes: voteA = β0 + β1log(expendA) + β2log(expendB) + β3prtystrA + u, where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures by Candidates A and B, and prtystrA is a measure of party strength for Candidate A (the percentage of the most recent presidential vote that went to A’s party). The sample regression function obtained from a sample of n = 173 observations is given by voteA \ = 45.08 + 6.083 ∗ log(expendA)–6.615 ∗ log(expendB) + 0.152 ∗ prtystrA, with the following standard errors and R-squared: se(βˆ
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.
The following model can be used to study whether campaign expenditures affect election outcomes:
voteA = β0 + β1log(expendA) + β2log(expendB) + β3prtystrA + u,
where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign
expenditures by Candidates A and B, and prtystrA is a measure of party strength for Candidate A (the
percentage of the most recent presidential vote that went to A’s party). The sample regression function
obtained from a sample of n = 173 observations is given by
voteA \ = 45.08 + 6.083 ∗ log(expendA)–6.615 ∗ log(expendB) + 0.152 ∗ prtystrA,
with the following standard errors and R-squared: se(βˆ
0) = 3.93, se(βˆ
1) = 0.382, se(βˆ
2) = 0.379, se(βˆ
3) =0.062, R2 = 0.793.
1) Interpret the sign and magnitude of the estimated effect of A’s expenditures on the outcome (β1). Do you think the estimated effect is the causal effect? Explain.
2) Interpret the explanatory power (R2) of the estimated model. Is it an evidence for causal effect of expendA
on voteA?
3) Based on the estimation results, discuss the statistical significance of the estimated coefficient for A’s
expenditure (at 0.05 significance level).
4) Is it a good idea to measure the expenditure variables in percentages of total expenditure of A and B.
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