1. The authors studied a number of variables they thought might be related to bone mineral...

  

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1. The authors 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) 54.4 59.3 74.6 62.0 73.7 70.8 66.8 66.7 64.7 71.8 69.7 64.7 62.1 68.5 58.3 BMD (g/cm) 1.15 1.26 1.42 1.06 1.44 1.02 1.26 1.35 1.02 0.91 1.28 1.17 1.12 1.24 1.00 A simple linear regression model was used to describe the relationship between weight at age 13 and BMD at age 27. a. What is the equation of the estimated regression line? Use it to obtain the predicted BMD when weight is 56. b. Give a point estimate of o. c. Test the significance of the intercept and slope. (a= 0.05) d. Find a 95% confidence interval for the intercept and slope parameters to check their significance. Compare the results with the ones found part c. e. What percentage of observed variation in BMD at age 27 can be explained by the simple linear regression model? f. Find a 95% confidence interval on the mean BMD, when the weight is equal to 72. g. Find a 95% prediction interval on the BMD, when the weight is equal to 57. Is your prediction interval wider than the corresponding confidence interval in part (f)? 1. The authors 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) 54.4 59.3 74.6 62.0 73.7 70.8 66.8 66.7 64.7 71.8 69.7 64.7 62.1 68.5 58.3 BMD (g/cm) 1.15 1.26 1.42 1.06 1.44 1.02 1.26 1.35 1.02 0.91 1.28 1.17 1.12 1.24 1.00 A simple linear regression model was used to describe the relationship between weight at age 13 and BMD at age 27. a. What is the equation of the estimated regression line? Use it to obtain the predicted BMD when weight is 56. b. Give a point estimate of o. c. Test the significance of the intercept and slope. (a= 0.05) d. Find a 95% confidence interval for the intercept and slope parameters to check their significance. Compare the results with the ones found part c. e. What percentage of observed variation in BMD at age 27 can be explained by the simple linear regression model? f. Find a 95% confidence interval on the mean BMD, when the weight is equal to 72. g. Find a 95% prediction interval on the BMD, when the weight is equal to 57. Is your prediction interval wider than the corresponding confidence interval in part (f)?