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 equation of a line in slope-intercept form?

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

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CCSS.8.EE.B.6

CCSS.8.F.A.3

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What does the slope in a linear regression equation represent?

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The slope represents the rate of change of the dependent variable for each unit change in the independent variable.

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CCSS.8.EE.B.5

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What is the purpose of the line of best fit?

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The line of best fit minimizes the distance between the data points and the line, providing the best approximation of the relationship between the variables.

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CCSS.8.EE.B.5

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How do you interpret the y-intercept in a linear regression model?

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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 a scatterplot?

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A scatterplot is a graphical representation of two variables, showing the relationship between them using points on a Cartesian plane.

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CCSS.8.SP.A.1

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What does it mean if the correlation coefficient is close to 1?

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A correlation coefficient close to 1 indicates a strong positive linear relationship between the two variables.

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CCSS.HSS.ID.B.5

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What is the formula for calculating the line of best fit?

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The formula for the line of best fit can be derived using the least squares method, resulting in the equation y = mx + b.

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CCSS.8.EE.B.5

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What is the significance of residuals in linear regression?

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

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CCSS.HSS.ID.B.6B

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How can you use linear regression to make predictions?

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You can use the linear regression equation to predict the value of the dependent variable for given values of the independent variable.