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Chapter 11: Correlation and Regression Back To Chapter

11.4: Regression Analysis

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Regression Analysis

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Regression analysis is a statistical method of developing a mathematical model to estimate a relationship between the variables. It is used to predict the value of a dependent variable based on another independent variable.

For example, consider a data set having a strong linear relationship with a correlation coefficient of 0.892.

A best-fit line passing through the scatter plot is the regression line.

The algebraic equation of the regression line is known as the regression equation.

It expresses the relationship between the carbon dioxide levels, x, the independent variable, and the annual temperature, y, the dependent variable.

Here, b₀ is the y-intercept, and b₁ is the slope of the regression line.

As the regression line shows a good fit, the regression equation can be used to predict the annual temperature for, say, a carbon dioxide level of 380 ppm.

This value is put in the regression equation to obtain the predicted annual temperature of 14.7 degrees Celsius.

11.4: Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.

In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:

Equation1

In the equation, Equation1 is the dependent variable, x is the independent variable, b₀ is the y-intercept, and b₁ is the slope of the regression line. is the estimated value of y. It is the value of y obtained using the regression line. It is not generally equal to y from data.

The regression equation can be used to calculate the dependent variable for a specific value of the independent variable.

This text is adapted from Openstax, Introductory Statistics, Section 12.3 The Regression Equation.

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Regression Analysis Statistical Tool Dependent Variable Independent Variable Line Of Best Fit Regression Equation Regression Line Y-intercept Slope Estimated Value Of Y Specific Value Of The Independent Variable

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