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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CCSS.8.SP.A.2

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What is the purpose of a best-fit line in linear regression?

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The best-fit line is used to make predictions about the dependent variable based on the values of the independent variable.

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CCSS.8.EE.B.5

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What does the slope of a linear regression line represent?

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The slope indicates the change in the dependent variable for a one-unit change in the independent variable.

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CCSS.8.EE.B.5

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What does the y-intercept of a linear regression line represent?

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The y-intercept is the value of the dependent variable when the independent variable is zero.

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CCSS.HSF.LE.B.5

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What is the formula for a simple linear regression?

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CCSS.8.EE.B.5

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What does the correlation coefficient (r) indicate in linear regression?

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The correlation coefficient indicates the strength and direction of the linear relationship between two variables, ranging from -1 to 1.

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CCSS.HSS.ID.C.8

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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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CCSS.8.SP.A.2

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What is the significance of the residuals in linear regression?

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Residuals are the differences between observed and predicted values; they help assess the fit of the model.

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CCSS.HSS.ID.B.6B

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What does it mean if the residuals are randomly distributed?

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Randomly distributed residuals suggest that the linear model is appropriate for the data.

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What is the purpose of the least squares method in linear regression?

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The least squares method minimizes the sum of the squares of the residuals to find the best-fitting line.