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 in linear regression?

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The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1. A value close to 1 indicates a strong positive correlation, while a value close to -1 indicates a strong negative correlation.

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CCSS.HSS.ID.C.8

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How do you interpret a correlation coefficient of 0.9746?

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A correlation coefficient of 0.9746 indicates a very strong positive linear relationship between the variables in the data set.

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CCSS.HSS.ID.B.5

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What is a residual in the context of linear regression?

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

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CCSS.HSS.ID.B.6B

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How do you calculate a residual?

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To calculate a residual, subtract the predicted value from the observed value: Residual = Observed Value - Predicted Value.

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CCSS.HSS.ID.B.6B

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What is the purpose of using Desmos for linear regression?

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Desmos is an online graphing calculator that allows users to visualize data, create graphs, and perform linear regression analysis easily.

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

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The equation of a best fit line is typically expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.5

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

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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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CCSS.8.EE.B.5

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

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The y-intercept (b) represents the 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 you use a linear regression model to make predictions?

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You can use a linear regression model to make predictions by plugging in values of the independent variable (x) into the regression equation to calculate the corresponding predicted value of the dependent variable (y).