Question

A water expert was asked whether the water table in a California community was falling. 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 might 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?

Answer 1

a. Yes, it can be concluded that the water table is falling because the coefficient of time is negative which means that as the time is passing or as number of years increasing, the height of the water table is falling and thus it can be concluded that the water table is falling.

b. No, this cannot be stated with certainty that years of low rainfall will cancel the years of heavy rainfall and thus impact of rainfall will be negated. This calls for separate accounting for monsoon months when rainfall is high and water table might increase in height and for summer months when the water table might decrease in height. Thus, two linear regression needs to be run in this case.