Concept explainers
The article “Drift in Posturography Systems Equipped with a Piezoelectric Force Platform: Analysis and Numerical Compensation” (L. Quagliarella, N. Sasanelli, and V. Monaco, IEEE Transactions on Instrumentation and Measurement, 2008:997–1004) reported the results of an experiment to determine the effect of load on the drift in signals derived from a piezoelectric force plate. The
x | y |
0.196 | –0.9710 |
0.245 | –0.9735 |
0.294 | –0.9694 |
0.343 | –0.9684 |
0.392 | –0.9624 |
0.441 | –0.9688 |
0.490 | –0.9519 |
0.539 | –0.9573 |
0.588 | –0.9515 |
- a. Compute the least-squares line for predicting y from x.
- b. Plot the residuals versus the fitted values. Does the least-squares line seem appropriate?
- c. Compute the least-squares line for predicting y from x2.
- d. Plot the residuals versus the fitted values. Does the least-squares line seem appropriate?
- e. For each model, find a 95% confidence interval for the
mean value of y when x = 0.32. Are the confidence intervals similar?
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- The article "Change in Creep Behavior of Plexiform Bone with Phosphate Ion Treatment" (R. Regimbal, C. DePaula, and N. Guzelsu, Bio-Medical Materials and Engineering, 2003:11-25) describes an experiment to study the effects of saline and phosphate ion solutions on mechanical properties of plexiform bone. The following table presents the yield stress measurements for six specimens treated with either saline (NaCI) or phosphate ion (Na,HPO4) solution, at a temperature of either 25°C or 37°C. (The article presents means and standard deviations only; the values in the table are consistent with these.) Solution Temperature NaCl Yield Stress (MPa) 138.40 130.89 94.646 96.653 116.90 88.215 25°C NaCl 37°C 92.312 147.28 116.48 88.802 114.37 90.737 Na,HPO, 25°C 120.18 129.43 139.76 132.75 137.23 121.73 Na,HPO4 37°C 123.50 128.94 102.86 99.941 161.68 136.44 a. Estimate all main effects and interactions. b. Construct an ANOVA table. You may give ranges for the P-values. Is the additive model…arrow_forwardThe article "Influence of Freezing Temperature on Hydraulic Conductivity of Silty Clay" (J. Konrad and M. Samson, Journal of Geotechnical and Geoenvironmental Engineering, 2000:180–187) describes a study of factors affecting hydraulic conductivity of soils. The measurements of hydraulic conductivity in units of 108 cm/s (y), initial void ratio (x), and thawed void ratio (x2) for 12 specimens of silty clay are presented in the following table. y 1.01 1.12 1.04 1.30 1.01 1.04 0.955 1.15 1.23 1.28 1.23 1.30 0.84 0.88 0.85 0.95 0.88 0.86 0.85 0.89 0.90 0.94 0.88 0.90 X1 0.81 0.85 0.87 0.92 0.84 0.85 0.85 0.86 0.85 0.92 0.88 0.92 X2 Fit the model y = Bo + fix1 + e. For each coefficient, test the null hypothesis that it is equal to 0. Fit the model y = Bo + Bzx2 + e. For each coefficient, test the null hypothesis that it is equal to 0. Fit the model y = Bo + BzX1 + Bzxz + e. For each coefficient, test the null hypothesis that it is equal to 0. d. Which of the models in parts (a) to (c) is…arrow_forward11-41/446 An article in The Journal of Clinical Endocrinology and Metabolism ["Simultaneous and Continuous 24-Hour Plasma and Cerebrospinal Fluid Leptin Measurements: Dissociation of Concentrations in Central and Peripheral Compartments" (2004, Vol. 89, pp. 258-265)] reported on a study of the demographics of simultaneous and continuous 24-hour plasma and cerebrospinal fluid leptin measurements. The data follow: y = BMI (kg/m2): 19.92, 20.59, 29.02, 20.78, 25.97, 20.39, 23.29, 17.27, 35.24 x = Age (yr): 45.5, 34.6, 40.6, 32.9, 28.2, 30.1, 52.1, 33.3, 47.0 11-41/446 y = BMI (kg/m?): 19.92, 20.59, 29.02, 20.78, 25.97, 20.39, 23.29, 17.27, 35.24 x = Age (yr): 45.5, 34.6, 40.6, 32.9, 28.2, 30.1, 52.1,33.3, 47.0 (a) Test for significance of regression using a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate o? and the standard deviation of B.arrow_forward
- 11-41/446 An article in The Journal of Clinical Endocrinology and Metabolism [“Simultaneous and Continuous 24-Hour Plasma and Cerebrospinal Fluid Leptin Measurements: Dissociation of Concentrations in Central and Peripheral Compartments" (2004, Vol. 89, pp. 258-265)] reported on a study of the demographics of simultaneous and continuous 24-hour plasma and cerebrospinal fluid leptin measurements. The data follow: y = BMI (kg/m2): 19.92, 20.59, 29.02, 20.78, 25.97, 20.39, 23.29, 17.27, 35.24 x = Age (yr): 45.5, 34.6, 40.6, 32.9, 28.2, 30.1, 52.1, 33.3, 47.0 (a) Test for significance of regression using a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate o? and the standard deviation of B. (c) What is the standard error of the intercept in this model?arrow_forwardThe article "Application of Analysis of Variance to Wet Clutch Engagement" (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117-125) presents the following fitted model for predicting clutch engagement time in seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m (x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4): y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x, The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate is 10 kN/s. b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not. Is it…arrow_forwardfind the least squares regression line equation from the given data.arrow_forward
- Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".† x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total SE Coef 2.483 6.464 R-Sq = 98.5% DF 1 9 10 SS 7639.0 117.0 7756.0 T 129.64 24.24 0.000 0.000 R-Sq (adj) = 98.3% MS 7639.0 13.0 F P 587.81 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t 半 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef P Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S = 3.60498 R-Sq = 98.5% R-Są (adj) - 98.3% SOURCE DF MS F P Regression 1 7639.0 7639.0 587.81 0.000 Residual Error 9 117.0 13.0 Total 10 7756.0 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 400 392 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total R-Sq= 98.5% DF SE Coef 2.483 6.464 1 9 10 SS 7639.0 117.0 7756..0 T 129.64 24.24 P 0.000 0.000. R-Sq (adj) 98.3% MS 7639.0 13.0 F 587.81 (a) Does the simple linear regression model appear to be appropriate?…arrow_forward
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