M4U8D2 Regression Lines and Residuals

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What is the Coefficient of Determination?

Back

The Coefficient of Determination is represented as r squared, indicating the proportion of variance in the dependent variable that can be explained by the independent variable.

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CCSS.HSS.ID.B.6B

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How do you calculate a residual?

Back

A residual is calculated as Observed - Predicted.

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CCSS.HSS.ID.B.6B

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What does the correlation coefficient represent?

Back

The correlation coefficient summarizes the direction and strength of the correlation between two variables.

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CCSS.HSS.ID.C.8

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What is the value of the correlation coefficient, r, in a linear regression model?

Back

The correlation coefficient, r, indicates the strength and direction of a linear relationship between two variables, with values ranging from -1 to 1.

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CCSS.HSS.ID.C.8

Front

In a study predicting crop yield based on fertilizer, what is the response variable?

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The response variable is the yield of the crop.

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CCSS.HSS.ID.C.9

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What does a positive correlation coefficient indicate?

Back

A positive correlation coefficient 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 coefficient indicate?

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A negative correlation coefficient 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 is the purpose of a regression line?

Back

A regression line is used to model the relationship between two variables and to make predictions.

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What is the formula for a simple linear regression line?

Back

The formula for a simple linear regression line is y = a + bx, where 'a' is the y-intercept and 'b' is the slope.

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CCSS.8.EE.C.8C

Front

What does the slope of a regression line represent?

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The slope of a regression line represents the change in the response variable for each one-unit change in the explanatory variable.

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CCSS.HSF-LE.A.1B