A water expert was asked whether increased water consumption in a California community was lowering its water table. To answer this question, the expert estimated a linear regression equation of the form
W = a + bt,
Where W = height of the water table and t = time measured from the start of the study period. (He used 10 years of water-table measurements.) The estimate for b was b = -.4 with a t-value of -1.4.
a. From this evidence, would you conclude that the water table was falling?
b. A second expert suggests yearly rainfall also may affect the water table.
The first expert agrees but argues that total rainfall fluctuates randomly from year to year. Rainy years would cancel out dry years and would not affect the results of the regression. Do you agree?