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

Question

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 36.8 49.3 47.6 41.7 44 50.3 40.2 36.1 45.3 49.8 46.7 37.1 Rate 1600 1030 1160 1280 1400 1340 1580 920 1120 980 1200 1160 Find the least-squares regression line for predicting metabolic rate from body mass. ANSWER: y^= equation editorEquation Editor

Explanation / Answer

The Well designed table for regression equation is given below

Here n = 12

so lets say line equation is y = a +bx

where y = metabolic rate and x - body mass

and a and b = line constants.

so by formulas

so a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

all the values are given above and putting all these values from the table, we ge

a = (14770 * 23264.2 - 524.9 * 642597)/ (12 * 23264.2 - 524.92 )

= (6313068.7)/ 3650.39= 1729.423

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

= [ (12 * 642597 - 524.9 * 14770)]/ [12 * 23264.2 - 524.92 ]

= -41609/3650.39

= - 11.40

so line equation is

y^ = 1729.42 - 11.40 xi

Mass (x) Rate(y) x^2 XY 36.8 1600 1354.24 58880 49.3 1030 2430.49 50779 47.6 1160 2265.76 55216 41.7 1280 1738.89 53376 44.0 1400 1936.00 61600 50.3 1340 2530.09 67402 40.2 1580 1616.04 63516 36.1 920 1303.21 33212 45.3 1120 2052.09 50736 49.8 980 2480.04 48804 46.7 1200 2180.89 56040 37.1 1160 1376.41 43036 sum 524.9 14770.0 23264.2 642597.0 Average 43.7 1230.8

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.