Question

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.)

Answer #1

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**

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=__?__
(Round to one decimal place as needed.)
β1≈b1=__?__
(Round to four decimal places as needed.)

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
3390 5220
3340 4630
2300 4070
2480 4120
3380 5020
(a) Treating the 7-day strength as the
explanatory variable, x, use technology to determine the estimates
of β0 and β1.
β0≈b0=1981.5
(Round to one decimal place as needed.)
β1≈b1=0.8833
(Round to four decimal places as needed.)
b) Compute the standard error...

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. Complete parts (a)
through (f) below. 7-Day Strength (psi), x 3380 3330 2620 2300
3390 28-Day Strength (psi), y 5020 4850 4190 4070 5220 (a)
Treating the 7-day strength as the explanatory variable, x, use
technology to determine the estimates of beta 0 and beta 1. beta
0almost equalsb 0equals nothing (Round to...

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. Complete parts (a)
through (f) below.
7-Day Strength (psi), x
24802480
33903390
23002300
33803380
26202620
Open in StatCrunch
+
Copy to Clipboard
+
Open in Excel
+
28-Day Strength (psi), y
41204120
52205220
40704070
50205020
41904190
(a) Treating the 7-day strength as the explanatory variable,
x, use technology to determine the estimates of...

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