Question

Question 3 (10pts) As part of a research program for a new cholesterol drug, a pharmaceutical company would like to investigate the relationship between the ages and LDL (low-density lipoprotein) cholesterol of men. The accompanying data set shows the ages and LDL cholesterol levels of seven randomly selected men. Construct a 95% prediction interval to estimate the LDL cholesterol level of a 29-year-old man. Cholesterol 144 Age 22 38 25 32 175 160 200 43 160 32 141 42 2 10 Determine the upper and lower limits of the prediction interval. (Round to one decimal place as needed.)

Answer 1

Here n= 7 у X-X y-у (x-x)? (y-7) (x-3)(y-ỹ) Ý y-y) 22 144 -11.4286 -26.0000 130.6122 676.0000 297.1429 151.0357 Residual = (y-ỹ) -7.0357 -2.5857 3.9861 49.5016 38 175 4.5714 5.0000 20.8980 25.0000 177.5857 6.6859 22.8571 84.2857 25 160 -10.0000 71.0408 100.0000 156.0139 15.8893 1047.8514 32 200 30.0000 2.0408 900.0000 -42.8571 32.3705 -8.4286 -1.4286 9.5714 -1.4286 43 160 -10.0000 91.6122 100.0000 841.0000 167.6295 185.8826 167.6295 184.2232 32 669.9073 709.1285 141 -95.7143 41.4286 342.8571 -29.0000 2.0408 -25.8826 -26.6295 25.7768 42 210 8.5714 40.0000 73.4694 1600.0000 664.4437 Total 234 1190 391.7143 4242.0000 650.0000 1190.0000 3163.4077 SST SSE =(x)/n = (234/7) = 33.4285714285714 y =(Ey)/n = (1190/7) = 170

b = Ξ Σ(- 3)(y-y). Σ(-x) 650/391.7143 = 1.659 a=y - bx = 170 - 1.659* (33.4286) = 114.53 The regression equation is, y = a+bx = 114.53+(1.659)x X y = 114.53+(1.659)x 162.651 29 y

SSE Standard Error of estimate = Se = 25.153162 n-2

2 X-X 1 SE for prediction=S, 1+=+ 27.47256 2 n Σ(x X-X

95% prediction Interval: Lower limit = ġ-t*(SE for prediction) = 92 Upper limit = ĝ+t*(SE for prediction) = 233.3