Question

# As concrete​ cures, it gains strength. The following data represent the​ 7-day and​ 28-day strength in...

As concrete​ cures, it gains strength. The following data represent the​ 7-day and​ 28-day strength in pounds per square inch​ (psi) of a certain type of concrete.

7-Day_Strength_(psi)_-_x   28-Day_Strength_(psi)_-_y
2300   4070
3380   5020
2620   4190
3390   5220
3330   4850

(a) Treating the​ 7-day strength as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

β0≈b0=1753.9​

(Round to one decimal place as​ needed.)

β1≈b1=0.9707

​(Round to four decimal places as​ needed.)

Se=150.6

​(Round to one decimal place as​ needed.)

​(c) A normal probability plot suggests that the residuals are normally distributed. Determine sb1.

Use the answer from part (b).

sb1=__?__

​(Round to four decimal places as​ needed.)

The excel output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 1753.8907 + 0.97074212 x
Sample size: 5
R (correlation coefficient) = 0.96699199
R-sq = 0.93507351
Estimate of error standard deviation: 150.58771

Parameter estimates:

Parameter Estimate Std. Err. Alternative DF T-Stat P-value
Intercept 1753.8907 448.72296 ≠ 0 3 3.908627 0.0297
Slope 0.97074212 0.14768328 ≠ 0 3 6.5731349 0.0072

Hence,

c) sb1 = Standard error of slope =  0.1477

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