Linear Regression and Residuals - Using Desmos

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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 does the correlation coefficient (r) indicate?

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The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. Values range from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

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CCSS.HSS.ID.C.8

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What is a residual in linear regression?

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A residual is the difference between the observed value and the predicted value from a regression model. It indicates how far off the model's prediction is from the actual data point.

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CCSS.HSS.ID.B.6B

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How do you interpret a positive residual?

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A positive residual indicates that the observed value is higher than the predicted value, suggesting that the model underestimates the actual data point.

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CCSS.HSS.ID.B.6B

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How do you interpret a negative residual?

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A negative residual indicates that the observed value is lower than the predicted value, suggesting that the model overestimates the actual data point.

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CCSS.HSS.ID.B.6B

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What is the equation of a linear regression line?

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the slope (m) represent in a linear regression equation?

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The slope (m) represents the change in the dependent variable (y) for a one-unit change in the independent variable (x). It indicates the direction and steepness of the line.

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CCSS.8.EE.B.5

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What does the y-intercept (b) represent in a linear regression equation?

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The y-intercept (b) represents the predicted value of the dependent variable (y) when the independent variable (x) is zero.

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CCSS.HSF.LE.B.5

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How can Desmos be used in linear regression analysis?

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Desmos is an online graphing calculator that allows users to input data points and generate a linear regression model, visualize the regression line, and calculate the correlation coefficient.

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What is the purpose of using a linear regression model?

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The purpose of using a linear regression model is to predict the value of a dependent variable based on the values of one or more independent variables, and to understand the relationship between them.

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CCSS.8.SP.A.3