CA Foundation · Quantitative Aptitude · Correlation and Regression
For 10 paired observations, Σx = 50, Σy = 80, Σxy = 450 and Σx² = 290. Using the regression line of y on x, what is the estimated y when x = 8?
The estimated y is 11.75. The slope is 500/400 = 1.25. With means 5 and 8, the line is y = 1.75 + 1.25x. Putting x = 8 gives 1.75 + 10 = 11.75.
- A11.75Correct
- B10.00
- C18.00
- D9.75
Explanation
byx = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) = (4500 − 4000)/(2900 − 2500) = 500/400 = 1.25. The means are x̄ = 5 and ȳ = 8, so the line is y = 8 + 1.25(x − 5) = 1.75 + 1.25x. At x = 8, y = 1.75 + 10 = 11.75. The value 10 omits the intercept, and 9.75 omits the slope term.
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