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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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.
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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