Linear Regression and Residuals - Using Desmos

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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.

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What is the equation of a linear regression model?

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What does the slope in a linear regression equation represent?

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The slope (m) represents the change in the dependent variable (y) for a one-unit change in the independent variable (x).

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What is the y-intercept in a linear regression equation?

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The y-intercept (b) is the value of the dependent variable (y) when the independent variable (x) is zero.

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What is a residual in the context of linear regression?

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How do you calculate a residual?

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What is the purpose of using Desmos for linear regression?

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Desmos is an online graphing calculator that allows users to visualize data, create linear regression models, and analyze relationships between variables.

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What is the correlation coefficient (r)?

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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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What does a correlation coefficient of 0.9998 indicate?

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A correlation coefficient of 0.9998 indicates a very strong positive linear relationship between the two variables.

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How do you interpret a positive residual?

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A positive residual indicates that the observed value is greater than the predicted value, suggesting that the model underestimates the actual data point.