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.

Tags

CCSS.8.SP.A.2

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What does the equation of a line in linear regression look like?

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The equation of a line in linear regression is typically expressed as 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 is the slope in a linear regression equation?

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The slope (m) represents the rate of change of the dependent variable (y) for each unit change in the independent variable (x).

Tags

CCSS.8.EE.B.5

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What is the y-intercept in a linear regression equation?

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The y-intercept (b) is the value of y when the independent variable (x) is zero; it represents the starting point of the line on the y-axis.

Tags

CCSS.HSF.LE.B.5

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How do you interpret the slope of the equation y = 1.5x + 12?

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In the equation y = 1.5x + 12, the slope of 1.5 indicates that for every 1 unit increase in x, y increases by 1.5 units.

Tags

CCSS.8.EE.B.5

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What is the purpose of finding the Line of Best Fit?

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The Line of Best Fit is used to predict the value of the dependent variable based on the independent variable, minimizing the distance between the data points and the line.

Tags

CCSS.8.EE.B.5

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How do you calculate the predicted value using a linear regression equation?

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To calculate the predicted value, substitute the value of the independent variable (x) into the linear regression equation and solve for y.

Tags

CCSS.8.EE.B.5

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

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

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CCSS.HSS.ID.C.8

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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 regression model.

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CCSS.HSS.ID.B.6B

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What is the formula for calculating the residual?

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The residual is calculated as: Residual = Observed value - Predicted value.

Tags

CCSS.HSS.ID.B.6B