5. Concrete. As concrete cures it gains strength. The table below lists the 7-da

Question

5. Concrete. As concrete cures it gains strength. The table below lists the 7-day strength (in pounds per square inch) and the 28-day strength( in pounds per square inch) of ten randomly selected samples 7-day 28-day strength strength 3390 5220 430 4640 2890 4620 3330 4850 480 3380 5020 890 2620 4190 660 46 (a) What is the value of r? (b) Calculate the coefficient of determination? (c) Interpret the coefficient of determination. (d) Find the standard error of estimate, se (e) Use regression to predict the 28-day strength of concrete with a 7-day strength of 3000 pounds per square inch (f) Construct a 95% prediction interval for the population mean 28-day strength for concrete with a 7-day strength of 3000 pounds per square inch.

Explanation / Answer

SolutionA:

Correlation coefficient=r=0.7584

there is a strong positive relationshi between 7-day strength and 28 day strength.

Solutionb:

coeffcient of determination =r sq=r*r

=0.758409*0.758409

=0.575184

=0.575184*100=57.52%

Solutonc:

57.52% variation in 28-day strength is explaained by 7-day strength .

Good model

Solutiond:

standard errorr of estmate=271.0423

Solutione:

the regression equation is

y=2675.562+0.676419x

y=2675.562+0.676419*3000

y=4704.819

the predicted 28 day strength of concrete is 4704.819

Regression Statistics Multiple R 0.758409 R Square 0.575184 Adjusted R Square 0.522082 Standard Error 271.0423 Observations 10

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