Chapter 14.3, Problem 38E

When Coastal power stations take in large amounts of cooling water, it is inevitable that a number of fish are drawn in with the water. Twenty-six observations from the article “Multiple Regression Analysis for Forecasting Critical Fish Influxes at Power Station Intakes” (Journal of Applied Ecology [1983]: 33–42) were used to fit a multiple regression model relating y = Number of fish taken in to the independent variables x₁ = Water temperature (°C), x₂ = Number of pumps running, x₃ = Sea State (taking values 0, 1, 2, or 3), and x₄ = Speed (knots). Partial Minitab output follows:

The regression equation is Y = 92.0 − 2.18X1 − 19.2X2 − 9.38X3 + 2.32X4

s = 10.53 R–sq = 39.0% R–sq(adj) = 27.3%

1. a. Construct a 95% confidence interval for β₃, the coefficient of x₃ = sea State. Interpret the resulting interval.
2. b. Construct a 90%’ confidence interval for the mean change in y associated with a 1° increase in temperature when number of pumps, sea State, and speed remain fixed.