Year 2008 2009 2010 2011 2012 2013 Salary, y | 2.93 3.00 3.01 3.10 3.21 3.39
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 table shows the average salaries y (in millions of dollars) of Major League Baseball players on opening day of baseball season from 2008 through 2013. (Source: Major League Baseball)
(a) Find the least squares regression line for the data. Let x represent the year, with x = 8 corresponding to 2008.
(b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part (a)?
(c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.
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