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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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) indicates 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 a positive slope in a linear regression?

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A positive slope indicates that as the independent variable increases, the dependent variable also increases.

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CCSS.HSF.LE.B.5

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How do you interpret a negative slope in a linear regression?

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A negative slope indicates that as the independent variable increases, the dependent variable decreases.

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CCSS.8.EE.B.5

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What does a correlation coefficient (r) of 0.28 indicate?

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A correlation coefficient of 0.28 indicates a weak positive relationship between the two variables.

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CCSS.HSS.ID.B.5

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What does a correlation coefficient (r) of -0.86 indicate?

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A correlation coefficient of -0.86 indicates a strong negative relationship between the two variables.

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CCSS.HSS.ID.B.5

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How can you calculate the expected value using a linear regression equation?

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

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What is the purpose of linear regression in real-world applications?

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Linear regression is used to predict outcomes, identify trends, and understand relationships between variables in various fields such as economics, biology, and social sciences.