Linear Regression

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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 (y) and one or more independent variables (x) by fitting a linear equation to observed data.

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What is the slope (m) in a linear equation?

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The slope (m) indicates the rate of change of the dependent variable (y) with respect to the independent variable (x). It shows how much y changes for a one-unit increase in x.

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What is the y-intercept (b) in a linear equation?

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The y-intercept (b) is the value of y when x is 0. It represents the point where the line crosses the y-axis.

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What does the correlation coefficient (r) indicate in Linear Regression?

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The correlation coefficient (r) measures the strength and direction of the 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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How do you interpret an r value of 0.9959?

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An r value of 0.9959 indicates a very strong positive linear relationship between the independent and dependent variables.

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What is the purpose of using a graphing calculator like Desmos in Linear Regression?

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A graphing calculator like Desmos helps visualize data points, fit a line to the data, and extract key values such as slope (m), y-intercept (b), and correlation coefficient (r).

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What is the significance of the best fit line in Linear Regression?

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The best fit line minimizes the distance between the observed data points and the line itself, providing the most accurate representation of the relationship between the variables.

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What does it mean if the slope (m) is positive?

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If the slope (m) is positive, it means that as the independent variable (x) increases, the dependent variable (y) also increases.

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What does it mean if the slope (m) is negative?

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If the slope (m) is negative, it means that as the independent variable (x) increases, the dependent variable (y) decreases.