Simple Linear Regression Model

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Intro In today’s world, most of the managerial decisions are based on the relationship of two or more variables. The primary goal of quantitative analysis is to use current information about a phenomenon to predict its future behavior. In our case, we act as a general manager from the National Hockey League (NHL) and are trying to find out if there is a relationship between the annual salary paid for a player and his offensive total production represented by the amount of points per game he makes throughout an entire season of 82 games. Simple Linear Regression Model While various non-linear forms may be used to analyze a data sample, simple linear regression model is the most common. Simple regression analysis is a statistical tool that gives us the ability to estimate the mathematical relationship between a dependent variable (called y) and an independent variable ( called x). The dependent variable is the variable for which we want to make a prediction. As mentioned earlier, our dependent variable is the annual salary of the player and the independent variable is its total offensive production calculated in points. Moreover, the equation describing how Y is related to X is called the Regression Model and is represented as follows: y = β0 + β1x + ε. The model’s parameters are β0 and β1 and ε represents the error term, which accounts for the variability in y that cannot be demonstrated by the linear relationship between x and y. Based on that model, the simple linear regression equation becomes: E(y) = β0 + β1x. The graph of such a regression equation is a straight line where β0 is the y-intercept point of the regression line, β1 is the slope and E(y) is the expected value of y for a given value of x. However, in practice, the parameters are not known and have to be estimated using a sample data. Once the data are gathered and typed on the

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