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We have data on the lean body mass and resting metabolic rate for 12 women who...

We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate, in calories burned per 24 hours, is the rate at which the body consumes energy.

Mass 48.7 42.2 49.9 40.4 47.6 45.2 40.7 47.9 45.7 51.5 36.6 48.6
Rate 1040 960 1570 1190 1480 980 950 1000 1400 1500 1030 1220


Find the least-squares regression line for predicting metabolic rate from body mass.
ANSWER: y^=

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Solution:

Step 1: Find X Y and X as it was done in the table below 48.7 42.2 49.9 40.4 47.6 45.2 40.7 47.9 45.7 51.5 36.6 48.6 1040 960 1570 1190 1480 980 950 1000 1400 1500 1030 1220 50648 40512 78343 48076 70448 44296 38665 47900 63980 77250 37698 59292 X. X 2371.69 1780.84 2490.01 1632.16 2265.76 2043.04 1656.49 2294.41 2088.49 2652.25 1339.56 2361.96 Step 2: Find the sum of every column: ΣΧ-545, ΣΥ-14320. Σ X.Y -657108, ΣΧ2-24976.66 Step 3: Use the following equations to find a and b y Y . Σ x2-y X-y XY 14320-24976.66-545-657108 12.24976.66-5452 n . ΣΧΥ-ΣΧ. ΣΥ 12 . 657108-545 . 14320 12 -24976.66 - (545) Step 4: Substitute a and b in regression equation formula y = -169.982 + 30.018-xleast-squares regression line for predicting metabolic rate from body mass = \hat{y} = -169.982 + 30.018 (x)

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