The regression line minimizes total squared vertical distance to the data. The gold marker shows the predicted value for the subject.
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Solution Roadmap
Flowchart for Solving This Linear Regression — Predict a Value Problem
1 · Gather the Sums and Means
From the 5 paired (x, y) data points, collect the running totals: Σx, Σy, Σx², Σxy, and the means x̄ and ȳ. These ingredients feed every formula in the rest of the regression.
2 · Build the Regression Line (slope b, intercept a)
Compute the slope (b) using the corrected sums of squares, then the y-intercept (a) using b and the means. Together they define the line ŷ = a + bx that best fits the data — the one minimizing total squared vertical distance.
3 · Predict the Subject’s Value
Plug the subject property’s x-value into ŷ = a + bx to get the predicted y for the subject. This is the whole payoff of regression: turning the pattern in your comparables into a number for the subject.
4 · Check the Correlation (r)
Compute the correlation coefficient r. Values close to +1 or −1 mean the line fits well and the prediction is trustworthy; values near 0 mean the data is scattered and the prediction has wide uncertainty. Always check r before relying on the prediction.