Here is a regression model in which the variable Alkali has been included in the model from Exercise 37:

a) State the null and alternative hypotheses about the coefficient of pH in this regression.
b) Assuming that the assumptions for regression inference are reasonable, test the hypothesis and state your conclusion.

c) Account for any differences with the conclusion you drew in exercise 37.
Here is a partial regression plot for the coefficient of Alkali:

d) What is the least squares slope of the partial regression plot? How do you know?
e) What effect does the point on the far left of the plot have on the coefficient of Alkali?

Data From Exercise 37

Biologists studying the effects of acid rain on wildlife  collected data from 172 streams in the Adirondack Mountains.  They recorded the pH (acidity) of the water and the BCI,  a measure of biological diversity. Here’s a scatterplot of  BCI against pH for the 163 streams for which we have these  data:

Response variable is: BCI R squared = 37.8% s = 130.1 with 163 3 160 degrees of freedom Coefficient 1641.48 -28.9009 Variable Intercept pH Alkali -1.45740 SE(Coeff) t-ratio 271.1 6.06 39.92 0.2774 -0.724 -5.25 P-value