A pile of sand on your local beach has no strengthand can be knocked down by a toddler with a lightkick. Sandstones, however, have a great variety ofstrength. “Certain horizons in the local CretaceousDakota sandstones, can be easily broken and crumbledby hand, while other horizons require a hammer and a good strong blow.” A coloration difference indi-cates a difference in the amount of cementation. The more iron oxide cement the darker and the strongerthe sandstone. A geologist collected data to study therelationship between porosity and sandstone strength.Based on those data, the least squares regression line is yn = 20560 - 1344.4x, where x is the percent of poros-ity and y is unconfined compressive sandstone strength measured in psi (pounds per square inch). Which of thefollowing best describes the meaning of the slope of theleast squares regression line?a) For each increase of 1 psi in strength, the estimatedporosity is expected to decrease by 1344.4%.b) For each increase of 1% in porosity, the estimatedstrength is expected to increase by 20560 psi.c) For each increase of 1% in porosity, the estimatedstrength is expected to increase by 1344.4 psi.d) For each increase of 1% porosity, the estimatedstrength is expected to decrease by 1344.4 psi.e) For each increase of 1% in porosity, the estimatedstrength is expected to increase by 19,215.6 psi.

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A pile of sand on your local beach has no strength
and can be knocked down by a toddler with a light
kick. Sandstones, however, have a great variety of
strength. “Certain horizons in the local Cretaceous
Dakota sandstones, can be easily broken and crumbled
by hand, while other horizons require a hammer and
a good strong blow.” A coloration difference indi-
cates a difference in the amount of cementation. The
more iron oxide cement the darker and the stronger
the sandstone. A geologist collected data to study the
relationship between porosity and sandstone strength.
Based on those data, the least squares regression line is
yn = 20560 - 1344.4x, where x is the percent of poros-
ity and y is unconfined compressive sandstone strength
measured in psi (pounds per square inch). Which of the
following best describes the meaning of the slope of the
least squares regression line?
a) For each increase of 1 psi in strength, the estimated
porosity is expected to decrease by 1344.4%.
b) For each increase of 1% in porosity, the estimated
strength is expected to increase by 20560 psi.
c) For each increase of 1% in porosity, the estimated
strength is expected to increase by 1344.4 psi.
d) For each increase of 1% porosity, the estimated
strength is expected to decrease by 1344.4 psi.
e) For each increase of 1% in porosity, the estimated
strength is expected to increase by 19,215.6 psi.
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