Regression Equations

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What is a regression equation?

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A regression equation is a mathematical formula that describes the relationship between a dependent variable and one or more independent variables.

Tags

CCSS.8.SP.A.2

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What does the y-intercept represent in a regression equation?

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The y-intercept is the value of the dependent variable when all independent variables are equal to zero.

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CCSS.HSF.LE.B.5

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What is the purpose of the correlation coefficient (r)?

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The correlation coefficient measures the strength and direction of a linear relationship between two variables.

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CCSS.HSS.ID.C.8

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What does a correlation coefficient of r = 0 indicate?

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A correlation coefficient of r = 0 indicates no linear relationship between the two variables.

Tags

CCSS.HSS.ID.B.5

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What does a positive correlation coefficient indicate?

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A positive correlation coefficient indicates that as one variable increases, the other variable also tends to increase.

Tags

CCSS.HSS.ID.B.5

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What does a negative correlation coefficient indicate?

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A negative correlation coefficient indicates that as one variable increases, the other variable tends to decrease.

Tags

CCSS.HSS.ID.B.5

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What is the difference between linear and non-linear regression?

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Linear regression models a straight-line relationship, while non-linear regression models relationships that are curved or not straight.

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What is the formula for a simple linear regression equation?

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The formula is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.5

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What does the slope (m) in a 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.

Tags

CCSS.8.EE.B.5

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What is the purpose of residuals in regression analysis?

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Residuals are the differences between observed and predicted values, used to assess the accuracy of the regression model.

Tags

CCSS.HSS.ID.B.6B