Concept explainers
a.
Construct a linear regression model for the data.
Test whether there is enough evidence to conclude that
Test whether there is enough evidence to conclude that
b.
Construct a quadratic regression model for the data.
Test whether there is enough evidence to conclude that
Test whether there is enough evidence to conclude that
Test whether there is enough evidence to conclude that
c.
Construct a cubic regression model for the data.
Test whether the coefficients are significantly different from zero.
d.
Find the best model among the three models obtained in part (a), part (b) and part (c).
e.
Estimate the flow rate of paraffinic hydrocarbons when the specific gravity is 0.83 using the most appropriate method.
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Statistics for Engineers and Scientists
- In "Orthogonal Design for Process Optimization and Its Application to Plasma Etching" (Solid State Technology, May 1987), G. Z. Yin and D. W. Jillie describe an experiment to determine the effect of C2Fe flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below. Observations C„F. Flow (SCCM) 2 3 4 5 125 2.5 4.4 2.6 3.2 3.2 4.0 160 4.8 4.4 4.8 4.2 3.6 4.2 200 4.6 3.3 2.8 3.4 4.2 5.3 (a) Does C,F, flow rate affect etch uniformity? Construct box plots to compare the factor levels and perform the analysis of variance. Use a = 0.05. There is that flow rate affects etch uniformity. (b) Do the residuals indicate any problems with the underlying assumptions? No. Statistical Tables and Charts Yes.arrow_forwardNeed help with (c) and (d) Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m3): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a…arrow_forward17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Countarrow_forward
- Q3) An experiment was carried out to investigate variation of solubility of chemical X in water. The quantities in kg that dissolved in 1 liter at various temperatures are show in the table (1). Table (1) Temperature C Mass of X 2.1 2.6 2.9 3.3 15 20 25 30 35 4 50 5.1 70 7 Use the proper methods to answer the following questions: a) Draw a scatter diagram to show the data. b) Estimate the temperature based on the mass of X. c) What quantity might be expected to dissolve at 42 C? Find the quantity that your cquation indicates would dissolve at 10 C and comment on your answer.arrow_forwardThe article "Simulation of the Hot Carbonate Process for Removal of CO, and H,S from Medium Btu Gas" (K. Park and T. Edgar, Energy Progress, 1984:174–180) presents an equation used to estimate the equilibrium vapor pressure of CO, in a potassium carbonate solution. The actual equilibrium pressure (in kPa) was measured in nine different reactions and compared with the value estimated from the equation. The results are presented in the following table: Reaction Estimated Experimental Difference 45.10 42.95 2.15 2 85.77 79.98 5.79 3 151.84 146.17 5.67 4. 244.30 228.22 16.08 5 257.67 240.63 17.04 6 44.32 41.99 2.33 84.41 82.05 2.36 8 150.47 149.62 0.85 253.81 245.45 8.36 Find a 95% confidence interval for the mean difference between the estimated and actual pressures.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".† 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_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".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_forwardFor steady-state water flow in a circular pipe made of concrete The following data have been collected: PIPE DIAMETER 0.3 EXPERIMENT SLOPE m/s VOLUMETRIC 1 0.001 0.04 2 0,6 0,.001 0,24 0.9 0,001 0,69 4 0.3 0,01 0,13 0.6 0,01 0.82 6. 0,9 0,01 2,38 7 0,3 0.05 0,31 8. 0.6 0.05 1.95 0,9 0.05 5.66 Determine the parameters (a0, a1 and a2) in the equation for the relation between Volumetric flow, Slope and Pipe Diameter using nonLinear Regression analysis Q = a,Dª S°:arrow_forwardThis dataset includes measurements of soil temperature and soil respiration at three places along the riverbank (upper, mid, and lower; the upper site is far away from water and the lower site is close to water). Please help describe and interpret the results below:arrow_forward
- The article "Experimental Measurement of Radiative Heat Transfer in Gas-Solid Suspersion Flaw System" (G. Han, K. Tuxla, and J. Chen, AChe Journal, 2002:1910-1916) discusses the a radiometer. Several measurements were made on the electromotive force readings of the radiometer (in volts) and the radiation flux (in kilowatts per square meter). Signal Output, x Heat Flux, y Predicted/Fitted Residual 1.08 15 2.42 31 4.17 51 4,46 55 5.17 67 6.92 89 For this data, the least squares line is = 0.153 + 12.679 x. Find the predicted/fitted values for each observed x value and find the residual for each observed x value. What is the predicted value of a Signal Output of 5.17? Round your answer to 3 decimal places.arrow_forwardPlease show me your solutions and interpretations. Show the completehypothesis-testing procedure.An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59–75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5 °C using α = 0.05.arrow_forwardThe Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST RBOT 4200 370 TOST RBOT 3575 3750 3700 340 375 315 4050 350 4870 4475 3450 400 375 285 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) 2795 195 2725 3750 220 345 3275 290 Interpret the value of the sample correlation coefficient. O The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT. (b) How…arrow_forward
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