Define Regression Line

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Examlex · Accepted Answer

The Answer is A regression line, also known as a line of best fit, is a straight line that best represents the data on a scatter plot. This line is used in regression analysis, which is a statistical method for modeling the relationship between a dependent variable and one or more independent variables.

The purpose of the regression line is to predict the value of the dependent variable based on the values of the independent variable(s). The line is calculated using the least squares method, which minimizes the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line.

In the simplest form of regression analysis, linear regression, the regression line has the equation:

Y = a + bX + ε

where:
- Y is the dependent variable,
- X is the independent variable,
- a is the y-intercept (the value of Y when X = 0),
- b is the slope of the line (the change in Y for a one-unit change in X),
- ε is the error term (the difference between the observed values and the values predicted by the line).

The coefficients a and b are determined during the regression analysis such that they provide the best fit for the data points. The goodness of fit of the regression line is often evaluated using the coefficient of determination (R²), which measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

In summary, a regression line is a statistical tool that represents the relationship between variables and is used to predict outcomes. It is a foundational concept in many fields that require data analysis, including economics, biology, engineering, and social sciences.

Define Regression Line

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