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 and one or more independent variables by fitting a linear equation to observed data.

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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 y = mx + b, where m is the slope and b is the y-intercept.

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What does the slope in a linear regression equation represent?

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The slope represents the rate of change of the dependent variable for each unit change in the independent variable.

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What does the y-intercept in a linear regression equation represent?

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The y-intercept represents the value of the dependent variable when the independent variable is zero.

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How do you find the line of best fit?

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The line of best fit is found using methods such as least squares, which minimizes the sum of the squares of the vertical distances of the points from the line.

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What is the purpose of the line of best fit?

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The purpose of the line of best fit is to provide a predictive model that can be used to estimate values of the dependent variable based on the independent variable.

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What is a residual in linear regression?

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A residual is the difference between the observed value and the predicted value from the regression line.

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How can you use a line of best fit to make predictions?

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You can use the line of best fit to make predictions by substituting the value of the independent variable into the regression equation to find the corresponding dependent variable value.

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What is the significance of R-squared in linear regression?

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R-squared indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

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What is the formula for calculating the slope (m) in linear regression?

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The formula for calculating the slope (m) is m = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2), where N is the number of data points.