Representative data on x = carbonation depth (in millimeters) and y = strength (in megapascals) for a sample of concrete core specimens taken from a particular building were read from a plot in the article “The Carbonation of Concrete Structures in the Tropical Environment of Singapore” (Magazine of Concrete Research [1996]: 293-300): Depth, x 8.0 20.0 20.0 30.0 35.0 40.0 50.0 55.0 65.0 Strength, y 22.8 17.1 21.1 16.1 13.4 12.4 11.4 9.7 6.8 a. Construct a scatterplot. Does the relationship between carbonation depth and strength appear to be linear? Yes, the relationship between carbonation depth and strength appears to be linear however it is a negative linear relation. b. Find the equation of the of the least-squares line. c. What would you predict for strength when carbonation depth is 25 mm? d. Explain why it would not be reasonable to use the least-squares line to predict strength when carbonation depth is 100 mm.
5.25. Representative data on x = carbonation depth (in millimeters) and y = strength (in megapascals) for a sample of concrete core specimens taken from a particular building were read from a plot in the article “The Carbonation of Concrete Structures in the Tropical Environment of Singapore” (Magazine of Concrete Research [1996]: 293-300):
Depth, x 8.0 20.0 20.0 30.0 35.0 40.0 50.0 55.0 65.0
Strength, y 22.8 17.1 21.1 16.1 13.4 12.4 11.4 9.7 6.8
a. Construct a scatterplot. Does the relationship between carbonation depth and strength appear to be linear?
Yes, the relationship between carbonation depth and strength appears to be linear however it is a negative linear relation.
b. Find the equation of the of the least-squares line.
c. What would you predict for strength when carbonation depth is 25 mm?
d. Explain why it would not be reasonable to use the least-squares line to predict strength when carbonation depth is 100 mm.
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