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 written 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 a linear regression line?

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The slope 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 purpose of finding the line of best fit?

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The line of best fit minimizes the distance between the data points and the line, providing the best approximation of the relationship between the variables.

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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; it measures the error in the prediction.

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What does it mean if the residuals are randomly scattered?

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If the residuals are randomly scattered around zero, it indicates that the linear model is a good fit for the data.

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What is the formula for calculating the slope in linear regression?

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The slope (m) can be calculated using the formula: m = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2), where N is the number of data points.

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What is the significance of the correlation coefficient in linear regression?

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The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, ranging from -1 to 1.