Linear Regression and Transformations

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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.

Tags

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 given by: 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 change in the dependent variable for a one-unit change in the independent variable.

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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 observed data points and the line itself, providing the best approximation of the relationship between variables.

Tags

CCSS.8.EE.B.5

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What is a power transformation?

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A power transformation is a technique used to stabilize variance and make the data more closely conform to a normal distribution by applying a power function to the data.

Tags

CCSS.HSS.ID.A.4

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What is a quadratic transformation?

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A quadratic transformation involves squaring the values of the variable to model non-linear relationships.

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What does it mean if there is no association between two variables?

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No association means that changes in one variable do not predict changes in another variable; there is no discernible relationship.

Tags

CCSS.HSF-LE.A.1B

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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 expected value of the dependent variable when all independent variables are equal to zero.

Tags

CCSS.HSF.LE.B.5

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What is the significance of R-squared in linear regression?

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R-squared indicates the proportion of variance in the dependent variable that can be explained by the independent variable(s) in the model.

Tags

CCSS.HSS.ID.B.6B

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What is the difference between positive linear and negative linear association?

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Positive linear association means that as one variable increases, the other variable also increases. Negative linear association means that as one variable increases, the other variable decreases.