The accompanying data was extracted from the article "Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083- H111."t The response variable is yield strength (MPa), and the predictor is temperature (°C). -s0 25 100 200 300 | 91.0 120.5 136.0 133.1 120.8 Here is Minitab output from fitting the quadratic regression model (a graph in the cited paper suggests that the authors did this). Predietor Coef SE Coef Conatant 111.277 2.100 52.98 0.000 0.32845 -0.0010050 temp 0.03303 9.94 0.010 tempaqd 0.0001213 -8.29 0.014 S - 3.44398 R-Sq - 98.18 R-Sq (adj) - 96.3 Analvete of variance
The accompanying data was extracted from the article "Effects of Cold and Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083- H111."t The response variable is yield strength (MPa), and the predictor is temperature (°C). -s0 25 100 200 300 | 91.0 120.5 136.0 133.1 120.8 Here is Minitab output from fitting the quadratic regression model (a graph in the cited paper suggests that the authors did this). Predietor Coef SE Coef Conatant 111.277 2.100 52.98 0.000 0.32845 -0.0010050 temp 0.03303 9.94 0.010 tempaqd 0.0001213 -8.29 0.014 S - 3.44398 R-Sq - 98.18 R-Sq (adj) - 96.3 Analvete of variance
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer all parts
Transcribed Image Text:The accompanying data was extracted from the article "Effects of Cold and
Warm Temperatures on Springback of Aluminum-Magnesium Alloy 5083-
H111."t The response variable is yield strength (MPa), and the predictor is
temperature (°C).
×| -so 25 100 200 300
91.0 120.5 136.0 133.1 120.8
Here is Minitab output from fitting the quadratic regression model (a graph
in the cited paper suggests that the authors did this).
Predictor
Coef
SE Coef
Constant
111.277
2.100
52.98
0.000
temp
0.32845
0.03303
9.94
0.010
tempaqd
-0.0010050
0.0001213
-8.29
0.014
S - 3.44398
R-Sq - 98.1%
R-Sq (adj) - 96.38
Analysis of Variance
Source
DF
MS
P
52.50
0.019
Regression
Residual Error
2
1245.39
622.69
2
23.72
11.86
Total
4
1269.11
(0) What percentage of observed variation in strength can be attributed to
the model relationship? (Round your answer to one decimal place.)
| %
(b) Carry out a test of hypotheses at significance level 0.05 to decide if the
quadratic predictor provides useful information over and above that
provided by the linear predictor.
State the appropriate null and alternative hypotheses.
O Ho: B2 = 0
H3: Bz > 0
O Ho: B2 = 0
Hạ: B2 < 0
O Ho: B2 = 0
O Ho: P2 = 0
Hạ: B2 # 0
%3D
State the appropriate test statistic and P-value from the output above.
Pvalue
State the conclusion in the problem context.
O Reject Ho. The quadratic term is not statistically significant in this
model.
O Fail to reject Ho. The quadratic term is not statistically significant in
this model.
O Fail to reject Ho. The quadratic term is statistically significant in this
model.
O Reject Ho. The quadratic term is statistically significant in this model.
(c) For a temperature of 100, - 134.07, Sp - 2.38. Estimate true average strength
when temperature is 100, in a way that conveys information about
precision and reliability. (Round your answers to one decimal place.)
) MPa
(a) Use the information in (c) to predict strength for a single observation to
be made when temperature is 100, and do so in a way that conveys
information about precision and reliability. (Round your answers to two
decimal places.)
) MPa
Compare this prediction to the estimate obtained in (c).
O The prediction interval is the same width as the confidence interval.
O The prediction interval is much narrower than the the confidence
interval.
O The prediction interval is much wider than the the confidence
interval.
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