Regression and Residuals - Using Desmos

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What is a linear regression model?

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A linear regression model 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 does the slope in a linear equation represent?

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The slope represents the rate of change of the dependent variable with respect to the independent variable. It indicates how much the dependent variable is expected to increase (or decrease) when the independent variable increases by one unit.

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What is the y-intercept in a linear equation?

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The y-intercept is the value of the dependent variable when the independent variable is zero. It represents the point where the line crosses the y-axis.

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What does the r-value (correlation coefficient) indicate?

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The r-value indicates the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

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What is a residual in regression analysis?

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A residual is the difference between the observed value and the predicted value of the dependent variable. It measures how well the regression model fits the data.

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What is interpolation in the context of regression?

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Interpolation is the process of estimating unknown values within the range of known data points. For example, predicting a value for x=8 when x-values in the data set include values around 8.

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What is extrapolation in regression analysis?

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Extrapolation is the process of estimating unknown values outside the range of known data points. For example, predicting a value for x=15 when the data set only includes values up to 10.

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How do you interpret the slope of the equation y = -2x + 7 in a real-world context?

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The slope of -2 indicates that for each hour of use, the amount of gas remaining in the lawnmower decreases by 2 gallons.

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What is the purpose of using Desmos for regression analysis?

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Desmos is an online graphing calculator that allows users to visualize data, create graphs, and perform regression analysis easily, making it a useful tool for students.

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What is the equation of a line in slope-intercept form?

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The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.