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 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.

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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).

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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 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 do you interpret the slope of a linear regression line?

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The slope indicates how much the dependent variable is expected to increase (or decrease) when the independent variable increases by one unit.

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What is the purpose of finding the line of best fit in linear regression?

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

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CCSS.8.SP.A.2

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What is a residual in linear regression?

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A residual is the difference between the observed value and the predicted value from the regression model.

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CCSS.HSS.ID.B.6B

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What does it mean if the residuals are randomly distributed?

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If the residuals are randomly distributed, it suggests that the linear regression model is a good fit for the data.

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CCSS.HSS.ID.B.6B

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

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R-squared is a statistical measure that represents the proportion of the variance for the dependent variable that's explained by the independent variable(s) in 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 by substituting the value of the independent variable into the equation.