AP Stats - Linear Regression Quick Review

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What is the equation of a linear regression line?

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The equation of a linear regression line is typically represented as ŷ = b0 + b1x, where ŷ is the predicted value, b0 is the y-intercept, b1 is the slope, and x is the independent variable.

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CCSS.HSS.ID.C.8

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What does the slope of a linear regression line represent?

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The slope (b1) of a linear regression line represents the average change in the dependent variable (y) for each one-unit increase in the independent variable (x).

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CCSS.8.SP.A.3

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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 a regression model, calculated as e = y - ŷ.

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CCSS.HSS.ID.B.6B

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How do you calculate the residual for a given data point?

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To calculate the residual for a data point, subtract the predicted value (ŷ) from the observed value (y): Residual = y - ŷ.

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CCSS.HSS.ID.B.6B

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

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The y-intercept (b0) represents the predicted 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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What is the purpose of a residual plot?

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A residual plot is used to assess the fit of a regression model by plotting the residuals on the y-axis against the independent variable (x) on the x-axis.

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CCSS.HSS.ID.B.6B

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What does a curved pattern in a residual plot indicate?

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A curved pattern in a residual plot suggests that the linear model may not be appropriate for the data, indicating a potential non-linear relationship.

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CCSS.HSS.ID.B.6B

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What is the correlation coefficient?

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The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

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CCSS.HSS.ID.C.8

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What does a correlation coefficient of 0.96 indicate?

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A correlation coefficient of 0.96 indicates a very strong positive linear relationship between the two variables.

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CCSS.HSS.ID.B.5

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What is the least-squares method in linear regression?

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The least-squares method is a statistical technique used to find the best-fitting line by minimizing the sum of the squares of the residuals.