Solved: Reconsider the filtration rate–moisture content

Chapter 12, Problem 45E

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Problem 45E

Reconsider the filtration rate–moisture content data introduced in Example 12.6 (see also Example 12.7).

a. Compute a 90% CI for  , true average moisture content when the filtration rate is 125.

b. Predict the value of moisture content for a single experimental run in which the filtration rate is 125 using a 90% prediction level. How does this interval compare to the interval of part (a)? Why is this the case?

c. How would the intervals of parts (a) and (b) compare to a CI and PI when filtration rate is 115? Answer without actually calculating these new intervals.

d. Interpret the hypotheses  , and then carry out a test at significance level .01.

Reference example 12.7

The residuals for the filtration rate–moisture content data were calculated previously. The corresponding error sum of squares is

The estimate of s2 is then  , and the estimated standard deviation is  . Roughly speaking, .665 is the magnitude of a typical deviation from the estimated regression line—some points are closer to the line than this and others are further away.

Computation of SSE from the defining formula involves much tedious arithmetic, because both the predicted values and residuals must first be calculated. Use of the following computational formula does not require these quantities.

This expression results from substituting  , squaring the summand, carrying through the sum to the resulting three terms, and simplifying. This computational formula is especially sensitive to the effects of rounding in , so carrying as many digits as possible in intermediate computations will protect against round-off error.