ESSENTIALS OF STATISTICS FOR BUSINESS AND ECONOMICS, 3e

by Anderson, Sweeney and Williams

Supplementary Problems for Chapter Twelve

  1. A medical laboratory at Duke University estimates the amount of protein in liver samples using regression analysis. A spectrometer emitting light shines through a substance containing the sample, and the amount of light absorbed is used to estimate the amount of protein in the sample. A new estimated regression equation is developed daily because of differing amounts of dye in the solution. On one day, six samples with known protein concentrations gave the absorbence readings shown below.

Absorbence Reading (xi)Milligrams of Protein (yi)

.5090

.75620

1.02040

1.40080

1.570100

1.790127

  1. Use these data to develop an estimated regression equation relating the light absorbence reading to milligrams of protein present in the sample.
  2. Compute r2. Would you feel comfortable using this estimated regression equation to estimate the amount of protein in a sample?
  3. In a sample just received, the light absorbence reading was .941. Estimate the amount of protein in the sample.

Correct answer:

  1. -54.844 + 98.803 x
  2. .9923
  3. 38.1
  1. A medical laboratory at Duke University estimates the amount of protein in liver samples using regression analysis. A spectrometer emitting light shines through a substance containing the sample, and the amount of light absorbed is used to estimate the amount of protein in the sample. A new estimated regression equation is developed daily because of differing amounts of dye in the solution. On one day, six samples with known protein concentrations gave the absorbence readings shown below.

Absorbence Reading (xi)Milligrams of Protein (yi)

.5090

.75620

1.02040

1.40080

1.570100

1.790127

Test whether the absorbence readings and the amount of protein are related at the .01 level of significance.

correct answer:

F = 21.20F* = 515.41reject Ho

or t = + 4.604t* = 22.70reject Ho

orp = .0000reject Ho