Question

Do heavier people burn more energy? A researcher collected data on the lean body mass (LBM) and resting metabolic rate (MR) for 10 individuals who were subjects of the study of dieting. LBM given in kilograms, is person’s weight leaving out all fat. Metabolic rate (MR) measured in calories burned per 24 hours. The researcher believes that LBM (independent) is an important influence on MR (dependent). Scores for variables body mass and metabolic rate are given in the following table (the scores have been rounded). The MR scores are in 10s scale.

Body mass (X)	Metabolic rate (Y)	X -X $q3R3Xsw8MET4L+cHnSwAAAABJRU5ErkJggg==$	Y -Y
36	99
55	142
48	140
42	141
50	150
32	91
42	110
51	134
41	120
33	103

1. Calculate X and Y

2. Complete the table and perform a regression analysis--calculate intercept a and slope b. Add or delete columns if necessary.

3. Write the regression equation for X and Y

4. Use correlation formula to obtain Pearson’s “R”

5. Explain the strength and the direction of the relationship between X and Y

6. Calculate “R²” for variables X and Y. What does R² tell us?

7. What would be the metabolic rate for a person with 35 LBM?

Answer 1

Answering the first four parts of the question as the terms and conditions allows me to answer atleast four for a valid answer.

papergrid Date: 11 b = 10x54201 - 430x1230 10x 19048 - (430) ² = 54 2010 - 528.400 190480 - 184900 13110 2:349 5580 e Thus the regression equation between a and y is given by axtb, ie, 21.92x4+ atba 21.97 +(2-349) x d. Pearson's correlation formula is. r = {(xi-i) (Yi-Y) J&cx-%28 yi-ý 12 = n(exy) (EXEY in ex² - (ex² [ney -[ey) ²] = 10 x 54201 - 430 x1230 (10x19048- (430) Clox 155902-(1230)?) 5420 10- 528900 1490480 - 1990) (1999020 - 1512900) 13110 5580 x 46120 13110 16042 12 - 0-8172 0.82 e. From the correlation value (+0.82), closer to 1), we can see that there is a strong positive relation between X andy

papergrid Date: 11 Body Mass (x) 36 55 م برا 140 ه ا Metabolic Raticy) ay 3564 142 7810 6720 141 5922 150 7500 91 2912_ the 4620 6834 120 4920 103 3399 1230 54201 x² y 1296 9801 3025 20164 2304 19600 1764__19881 2500 22500 1024 8281 1764 12100 2601 17956. 1681 14400 1089 10609 19048 155902 م م م 134 ه ة M (a) X = {xi = 36 +55+ ... +33 = 430 = 43 10 7 = EY - 99+ 142+ ... +103 = 1230 - 123 lo 10 (6) let the regression equation be given by y=a+bx yo anto, where a and b are the slope and intercept resp edively. The formulas for a and b are as follows: 322) - (x2 (Exy) N(Ex²) - (Ex7 and ben (Exy) - (Ex) (Ey (8x2) - (Ex) ² Here n-6, and all the other values are computed in the table. Substituting, we get oma (1230) (19048) – (430) 642012 10 (19048) - (43022 23429040 - 233 06430 190 480 - 184.900. 122610 - 21.97 5580