Least Square Linear Regressions

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What is the least squares method in linear regression?

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A statistical technique used to determine the best-fitting line by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the model.

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CCSS.HSF-LE.A.1B

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What is the explanatory variable in a regression analysis?

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The variable that is manipulated or changed to observe its effect on the response variable; also known as the independent variable.

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CCSS.HSS.ID.B.6B

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What does Y-hat (\hat{Y}) represent in regression analysis?

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The predicted value of the dependent variable (Y) for a given value of the independent variable (X).

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CCSS.HSF.LE.B.5

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What is the general form of a linear regression equation?

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CCSS.8.EE.B.5

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How do you interpret the slope (b) in a linear regression equation?

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The slope represents the change in the dependent variable (Y) for a one-unit increase in the independent variable (X).

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CCSS.HSF.LE.B.5

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What is the purpose of the intercept (a) in a linear regression equation?

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The intercept is the predicted value of Y when the independent variable X is zero.

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CCSS.HSF.LE.B.5

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What does it mean if a regression model has a high R-squared value?

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A high R-squared value indicates that a large proportion of the variance in the dependent variable is explained by the independent variable(s) in the model.

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CCSS.HSS.ID.B.6B

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What is a residual in the context of regression analysis?

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A residual is the difference between the observed value and the predicted value of the dependent variable; it represents the error in the prediction.

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CCSS.HSS.ID.B.6B

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What is the significance of the least squares criterion?

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The least squares criterion ensures that the best-fitting line minimizes the total squared differences between observed and predicted values, leading to the most accurate predictions.

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

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