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 does the equation of a line in linear regression look like?

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The equation of a line in linear regression is typically expressed as y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope in a linear regression equation?

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The slope (m) represents the rate of change of the dependent variable (y) for each 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 y when the independent variable (x) is zero; it represents the starting point of the line on the y-axis.

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How do you interpret the slope of the equation y = 1.5x + 12?

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In the equation y = 1.5x + 12, the slope of 1.5 indicates that for every 1 unit increase in x, y increases by 1.5 units.

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What is the purpose of finding the Line of Best Fit?

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The Line of Best Fit is used to predict the value of the dependent variable based on the independent variable, minimizing the distance between the data points and the line.

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How do you calculate the predicted value using a linear regression equation?

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To calculate the predicted value, substitute the value of the independent variable (x) into the linear regression equation and solve for y.

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What does it mean if the correlation coefficient is close to 1 in linear regression?

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A correlation coefficient close to 1 indicates a strong positive linear relationship between the independent and dependent variables.

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What is the significance of residuals in linear regression?

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Residuals are the differences between observed values and predicted values; they help assess the accuracy of the regression model.

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What is the formula for calculating the residual?

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The residual is calculated as: Residual = Observed value - Predicted value.