GATE 2022 BM – Question 50
Six subjects have systolic pressures in mmHg [120,90,100,110,140,130] and corresponding heart weights in grams [500,300,420,390,490,450]. Find the linear regression coefficient for estimating heart weight from pressure, to two decimals.
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Correct answer: 3.27 to 3.31
Explanation
Use the least-squares slope b=Σ(x−x̄)(y−ȳ)/Σ(x−x̄)² with pressure as x. Here x̄=115 and ȳ=425. The cross-product sum is 5750 and squared-pressure-deviation sum 1750. Thus b=5750/1750=3.285714, rounded to 3.29 g/mmHg. Reversing dependent and independent variables would give a different coefficient.