We are interested in looking at the effect of a baseball player’s free-agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not. 1. What is the conditional distribution of the variable High Salary when looking only at those who are free agents? 2. What is the conditional distribution of the variable High Salarywhen looking only at those who are not free agents? 3. What is the marginal distribution of High Salary
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.
We are interested in looking at the effect of a baseball player’s free-agent status on their salary. We look at 337 baseball players and categorize them as either having a high salary (above 2 million) or not, and as either being free agents or not.
1. What is the conditional distribution of the variable High Salary when looking only at those who are free agents?
2. What is the conditional distribution of the variable High Salarywhen looking only at those who are not free agents?
3. What is the marginal distribution of High Salary?
![Crosstabs
Case Processing Summary
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
High Salary * Free Agent
337
100.0%
0.0%
337
100.0%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fdf336d-4f09-474f-8885-c9f1cef645bf%2F450e059c-d0cc-45ff-b056-08e076e4beab%2Fbicjv5_processed.png&w=3840&q=75)
![High Salary * Free Agent Crosstabulation
Free Agent
Not Free Agent Free Agent
Total
High Salary Normal Salary Count
185
61
246
Expected Count
148.2
97.8
246.0
% within Free Agent
91.1%
45.5%
73.0%
High Salary
Count
18
73
91
Expected Count
54.8
36.2
91.0
% within Free Agent
8.9%
54.5%
27.0%
Total
Count
203
134
337
Expected Count
203.0
134.0
337.0
% within Free Agent
100.0%
100.0%
100.0%
Chi-Square Tests
Asymptotic
Significance (2- Exact Sig. (2-
sided)
Exact Sig. (1-
sided)
Value
df
sided)
Pearson Chi-Square
85.190°
1
.000
Continuity Correctionb
82.891
.000
1
Likelihood Ratio
86.872
1
.000
Fisher's Exact Test
.000
.000
Linear-by-Linear
Association
84.937
1
.000
N of Valid Cases
a. O cells (0.0%) have expected count less than 5. The minimum expected count is 36.18.
337
b. Computed only for a 2x2 table](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fdf336d-4f09-474f-8885-c9f1cef645bf%2F450e059c-d0cc-45ff-b056-08e076e4beab%2Fdjt8jco_processed.png&w=3840&q=75)
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