Suppose that the team owner is trying to decide whether to pay a particular free agent player. Based on the player's previous statistics, the owner thinks that the new player can help his team increase the number of wins but the new player is going to cost more than the player he will be replacing. The owner decides it is a good idea to sign the new player if he can be pretty sure that the coefficient is at least 0.20. When testing this hypothesis, what is the test statistic?
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.
26. Below is some of the regression output from a simple regression of the number of wins for a major league baseball team and the size amount of money the team is paying its players (expressed in millions of $'s)
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SUMMARY OUTPUT |
Wins v. Team Payroll |
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Regression Statistics |
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Multiple R |
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R Square |
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Adjusted R Square |
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Standard Error |
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Observations |
30 |
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ANOVA |
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df |
SS |
MS |
F |
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Regression |
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1032.6 |
1032.6 |
13.7 |
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Residual |
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2109.7 |
75.3 |
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Total |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
67.6 |
4.02 |
16.8 |
3.515E-16 |
59.4 |
75.9 |
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Payroll |
0.271 |
0.067 |
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0.0009 |
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0.387 |
Suppose that the team owner is trying to decide whether to pay a particular free agent player. Based on the player's previous statistics, the owner thinks that the new player can help his team increase the number of wins but the new player is going to cost more than the player he will be replacing. The owner decides it is a good idea to sign the new player if he can be pretty sure that the coefficient is at least 0.20. When testing this hypothesis, what is the test statistic? (please express your answer using 2 decimal places)
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