Linear Regression practice

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What is the equation of a linear regression line?

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What does the slope (m) represent in a linear regression equation?

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

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What does the y-intercept (b) represent in a linear regression 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 is the purpose of the least-squares method in linear regression?

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The least-squares method is used to find the best-fitting line by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line.

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What is the correlation coefficient (r) in linear regression?

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The correlation coefficient (r) measures 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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How do you interpret a correlation coefficient of 0.8?

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A correlation coefficient of 0.8 indicates a strong positive linear relationship between the two variables, meaning as one variable increases, the other variable tends to also increase.

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What is the line of best fit?

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The line of best fit is a straight line that best represents the data on a scatter plot. It is determined using linear regression and minimizes the distance between the line and the data points.

Front

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

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Front

What is the formula for calculating the y-intercept (b) in linear regression?

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Front

What is a residual in the context of linear regression?

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