The standard method of determining the water content of soil involves the removal of the soil and estimation of soil volume. Forest Engineering (July 1999) presented a method that does not require soil removal, i.e., an indirect method, called the radiation method. The new method utilizes the fact that water content is proportional to the number of thermalized hydrogen neutrons emitted from the soil. A sample of 56 soil cores were collected at a depth of 10 feet; for each core, the water content was determined using the standard method and the count of hydrogen neutrons determined by radiation. A simple linear regression of the data yielded the following results: 

ŷ = .088 + 1.36x,  r² = .84

where y = water content (grams per cubic centimeter) and x = count ratio (number of hydrogen neutrons divided by the standard count).

a. Interpret the estimated y-intercept of the least-squares line.

b. Interpret the estimated slope of the least-squares line.

c. The p-value for testing whether the slope is 0 was determined to be .0001. Interpret this result.

d. Interpret the value of r².