In statistics, a residual is defined as the difference between an observed value and a predicted value. Regression analysis is an attempt to fit a set of data to a line in the form of y = mx + b. However, this straight line cannot typically account for all of the data points, and an error, e, is added to the equation to account for this, making the true equation y = mx + b + e. The e is a measurement of the residual and takes on a different value for each value of x.
- Sample intercept
- Sample slope
- Observed value from data set
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Instructions
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1
Create your regression line in the form of y = mx + b + e, where m is your sample slope and b is your sample intercept. e, is the residual we will solve for.
Sample intercept: 437.4
Sample slope: 5.47
y = 5.47x + 437.4 + e
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2
Plug your observed values for x and y into the equation.
Observed x = 16
Observed y = 557.02
557.02 = 5.47(16) + 437.4 + e
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3
Solve for your residual, e.
557.02 = 5.47(16) + 437.4 + e
557.02 = 87.52 + 437.4 + e
557.02 = 524.92 + e
e = 32.1