Three market leaders in homeowners insurance in a state are State Farm, American Family Insurance Group, and Allstate. Based on data from a certain year, two relationships between the homeowners insurance percentage market shares are found to be as given below, where x, y, z, and w are the percentages of the market held by State Farm, American Family, Allstate, and other companies, respectively. x = −54 + 5y + z z = 9 − 2y + w Given that the four groups account for the entire market, obtain a third equation relating x, y, z, and w, and solve the associated system of three linear equations to show how the market shares of State Farm, American Family, and Allstate depend on the share held by other companies. (Express your answer in terms of w, where x = x(w), y = y(w), and z = z(w).) (x, y, z) = Which of the three companies' market share is most affected by the share held by other companies?
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.
x, y, z and w are the percentage share of the market held by State Farm, American Family, Allstate and other companies respectively. so,
also given that,
Now we have system of three linear equation in x, y, z which can be expressed in terms of w.
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