least squares regression line

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What is the least squares regression line?

Back

The least squares regression line is a statistical method used to determine the best-fitting line through a set of data points by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line.

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How do you make a prediction using the regression line?

Back

To make a prediction using the regression line, you plug in a value for x (the independent variable) into the regression equation and simplify to find the predicted value of y (y-hat).

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What does a correlation indicate about two variables?

Back

A correlation indicates that two variables are related, but it does not imply causation.

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CCSS.HSS.ID.C.9

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What does a negative correlation mean?

Back

A negative correlation means that as one variable increases, the other variable decreases.

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CCSS.HSS.ID.B.5

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What is extrapolation in the context of regression?

Back

Extrapolation is the use of a regression line for prediction outside the interval of x values used to obtain the line.

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CCSS.HSS.ID.B.6A

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What is the purpose of a scatter plot in regression analysis?

Back

A scatter plot visually represents the relationship between two variables, helping to identify patterns, trends, and correlations.

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What does it mean if a scatter plot shows no association?

Back

If a scatter plot shows no association, it means there is no discernible pattern or relationship between the two variables.

Tags

CCSS.HSS.ID.B.5

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What is the formula for the least squares regression line?

Back

The formula for the least squares regression line is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the slope in a regression line?

Back

The slope (m) indicates 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 does the y-intercept represent in a regression line?

Back

The y-intercept (b) represents the predicted value of y when x is zero.

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CCSS.HSF.LE.B.5