Question: No-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste, is beneficial in areas prone to excessive rainfall because of its excellent drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots" employed a least squares analysis in studying how y = porosity (%) is related to X = unit weight (pcf) in concrete specimens. Consider the following representative data.

Relevant summary quantities are

n = 15, \(\sum{{{y}_{i}}}=299\) , \(\sum{y_{i}^{2}}=6387.58\), \(\sum{{{x}_{i}}}=1640.8\), \(\sum{x_{i}^{2}}=180,004.78\), \(\sum{{{x}_{i}}{{y}_{i}}}=32,239.73\)

b) Interpret the slope of the least squares line. (Round your answer to four decimal places.)

The slope tells us that a one-pcf increase in the unit weight of a concrete specimen is associated with a ______ percentage point decrease in the specimen's predicted porosity.

c) Predict porosity when unit weight is 135? (Round your answer to two decimal places.)

d) Calculate the residual corresponding to the first observation. (Round your answer to two decimal places.)

Calculate the residual corresponding to the second observation. (Round your answer to two decimal places.)

(e) Calculate a point estimate of \(\sigma \) . (Round your answer to two decimal places.)

(f) What proportion of observed variation in porosity can be attributed to the approximate linear relationship between unit weight and porosity? (Round your answer to two decimal places.)

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