Question

The authors of the paper "Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake" studied a number of variables they thought might be related to bone mineral density (BMD). The accompanying data on x = weight at age 13 and y = bone mineral density at age 27 are consistent with summary quantities for women given in the paper. Weight (kg) BMD (g/cm2) 54.4 1.15 59.3 1.26 74.6 1.42 62.0 1.06 73.7 1.44 70.8 1.02 66.8 1.26 66.7 1.35 64.7 1.02 71.8 0.91 69.7 1.28 64.7 1.17 62.1 1.12 68.5 1.24 58.3 1.00 A simple linear regression model was used to describe the relationship between weight at age 13 and BMD at age 27. The following values are given for this data. a = 0.558 b = 0.009 n = 15 SSTo = 0.356 SSResid = 0.313 (a) What percentage of observed variation in BMD at age 27 can be explained by the simple linear regression model? (Round your answer to one decimal place.) % (b) Give an estimate of σ. (Round your answer to three decimal places.) Interpret this estimate. This is an average of bone mineral density values in the sample from the value predicted by the least-squares line. This is a typical deviation of a weight value in the sample from the value predicted by the least-squares line. This is a typical deviation of a bone mineral density value in the sample from the value predicted by the least-squares line. This is an average of weight values in the sample from the value predicted by the least-squares line. Correct: Your answer is correct. (c) Give an estimate of the average change in BMD associated with a 1 kg increase in weight at age 13. (Round your answer to three decimal places.) g/cm2 (d) Compute an estimate of the mean BMD at age 27 for women whose weight at age 13 was 56 kg. (Round your answer to three decimal places.) g/cm2

Answer 1

s Given, n= weight at age is y Bone mineral density at age 27 (BMD) be 0.009 a: 0.556 :15 . ssto 0.356 SsResid : 0.313. 0.356 To find a) At what percentage of obserbeel variation in sms at age 22 can be empliendo by simple linear regršsion model The coefficiend of determination (n?) which isoletineda ² ,- ssilesia 1. SSTO El caso 12 0.120786) ;. e., 12.14 of observed variation in Bad at age an can be explaned by the simple linear regression mode b). To find an estimation, is the estimated standerd deviation (se) Se sskosid 0.513 to Now, . n.2 0.313 = 0.387 15 -2 13

S. = 0.0 2407692 Se z 0.024 Hence, the estimated Standare! cleviation. Se: 0.002407692 o To live an estimate of the average change in BMD associated with one kg increase in weight at age is. An estimation of the average change in the BMD associated with a lkg increase in weight 13(n) is the slope of the regurssion line x andy. BMD (4): 0.558 +0.009(weight, nj flere 0.009 is the slope of the regurssion. d) Compute an estimate of the mean BMD at age 22 BMD EY) 0.558+ (0.009) (Weisht, n) weight is 55 kg .. BMD (y): 0.558 +(0.00%) (55) BMOCY) =-1.053) The mean of BMD at aze ar for women whose age is is was s5kg is ros3