The following approach was used to determine the effect of acid rain on agricultural production. U.S. Department of Agriculture statistics on crop production, fertilizer practices, insect control,...

The following approach was used to determine the effect of acid rain on agricultural production. U.S. Department of Agriculture statistics on crop production, fertilizer practices, insect control, fuel costs, land costs, equipment costs, labor costs, and so forth for each county in the geographical area of interest were paired with county-level estimates of average pH of rainfall for the year. A multiple regression analysis was run in which “production ($)” was used as the dependent variable and all input costs plus pH of rainfall were used as independent variables. A stepwise regression analysis was used with pH forced to be in all regressions. The partial regression coefficient on pH from the model chosen by stepwise regression was taken as the measure of the impact of acid rain on crop production.

(a) Discuss the validity of these data for establishing a causal relationship between acid rain and crop production.

(b) Suppose a causal effect of acid rain on crop production had already been established from other research. Discuss the use of the partial regression coefficient for pH from these data to predict the change in crop production that would result if rain acidity were to be decreased. Do you see any reason the prediction might not be valid?

(c) Suppose the regression coefficient for pH were significantly negative (higher pH predicts lower crop production). Do you see any problem with inferring that stricter government air pollution standards on industry would result in an increase in crop production?

(d) Do you see any potential for bias in the estimate of the partial regression coefficient for pH resulting from the omission of other variables?