Refer to the Journal of Engineering for Industry study of vehicle congestion in an automated warehouse, Exercise 10.73. The data on number of vehicles (x) and congestion time (y) are reproduced in the table. Consider the straight line model E(y) = β_o + β₁x.

a. Construct Y and X matrices for the data.

b. Find X'X and X'Y.

c. Find the least-squares estimates β̂ = (X'X)^-1X'Y.

d. Find SSE and s².

e. Conduct the test H_o: β₁ = 0 vs. H_a: β₁ > 0 at α = .01.

f. Find and interpret R².

g. Find and interpret a 99% prediction interval for y when x = 5.

Data from Exercise 10.73

Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese. (Journal of Applied Ecology, Vol. 32, 1995.) Goslings were deprived of food until their guts were empty, then were allowed to feed for 6 hours on a diet of plants or Purina Duck Chow. For each feeding trial, the change in the weight of the gosling after 2.5 hours was recorded as a percentage of initial weight. Two other variables recorded were digestion efficiency (measured as a percentage) and amount of acid-detergent fiber in the digestive tract (also measured as a percentage). The data for 42 feeding trials are saved in the SNOWGEESE file. 

Transcribed Image Text:

WAREHOUSE Number of Congestion Time, y Number of congestion Time, y Vehicles, x (minutes, hundredths) vehicles, x (minutes, hundredths) 1 9 2 2 10 4 3 2 11 4 4 1 12 4 5 1 13 3 6 1 14 4 7 15 5 8 3. 3.