Scatterplots, Linear Regression, and Residuals

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What is a scatterplot?

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A scatterplot is a graphical representation of two variables, showing the relationship between them using points on a Cartesian plane.

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CCSS.8.SP.A.1

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What does a positive correlation in a scatterplot indicate?

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A positive correlation indicates that as one variable increases, the other variable also tends to increase.

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CCSS.HSS.ID.B.5

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What does a negative correlation in a scatterplot indicate?

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A negative correlation indicates that as one variable increases, the other variable tends to decrease.

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CCSS.HSS.ID.B.5

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What does no correlation in a scatterplot indicate?

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No correlation indicates that there is no discernible relationship between the two variables.

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CCSS.HSF-LE.A.1B

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How do you calculate a residual?

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Residual = Actual value - Predicted value.

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CCSS.HSS.ID.B.6B

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What does a residual plot show?

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A residual plot shows the residuals on the vertical axis and the independent variable on the horizontal axis, helping to assess the fit of a regression model.

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What does it mean if a residual plot has no pattern?

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If a residual plot has no pattern, it suggests that the linear regression model is a good fit for the data.

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What does it mean if a residual plot shows a pattern?

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If a residual plot shows a pattern, it indicates that the linear regression model may not be appropriate for the data.

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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.

Tags

CCSS.8.SP.A.2

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What is the purpose of a trend line in a scatterplot?

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A trend line is used to summarize the relationship between the variables and can be used to make predictions.