Linear Regression

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What is Linear Regression?

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Linear Regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

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What does the equation of a line in linear regression look like?

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The equation of a line in linear regression is typically written as y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope in a linear regression equation?

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The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

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What is the y-intercept in a linear regression equation?

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The y-intercept (b) is the value of y when x is 0. It represents the starting point of the line on the y-axis.

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How do you interpret the coefficients in a linear regression equation?

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The coefficients in a linear regression equation indicate the strength and direction of the relationship between the independent variable(s) and the dependent variable.

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What is the purpose of calculating a linear regression equation?

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The purpose of calculating a linear regression equation is to predict the value of the dependent variable based on the values of the independent variable(s).

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What is the significance of the correlation coefficient in linear regression?

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The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.

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What does a correlation coefficient of 0 indicate?

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A correlation coefficient of 0 indicates no linear relationship between the independent and dependent variables.

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What is the difference between simple and multiple linear regression?

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Simple linear regression involves one independent variable, while multiple linear regression involves two or more independent variables.

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What is the residual in linear regression?

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A residual is the difference between the observed value and the predicted value of the dependent variable. It measures the error in the prediction.