Final answer:
To calculate the line of best fit, data is entered into a calculator or computer, a scatter plot is made, and the regression function finds the equation. The predicted value is found by substituting x into the equation, and the residual is the actual y-value minus the predicted y-value for the same x.
Step-by-step explanation:
To calculate the line of best fit, or the least-squares regression line, for a set of data, you would typically follow this process:
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- Enter the data into a calculator or computer.
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- Make a scatter plot of the data on the calculator or computer.
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- Use the regression function of the calculator or statistical software to obtain the equation of the line of best fit, rounding the coefficients to four decimal places.
To find the predicted value using the equation, you would:
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- Use the equation of the line of best fit.
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- Substitute the given x-value (e.g., for a specific pinky length or hours of sleep) into the equation.
To find the residual for a person who slept 5 hours, you would:
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- Calculate the predicted y-value (such as the predicted height or page cost) for x = 5 using the equation of the line of best fit.
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- Subtract the actual y-value corresponding to x = 5 from this predicted y-value to obtain the residual.
For example, if the equation of the line of best fit was y = mx + b and a person who slept 5 hours actually has a measured y-value of y_actual, then the predicted y-value would be y_predicted = m*5 + b. The residual would then be y_actual - y_predicted.