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The article “Mechanistic-Empirical Design of Bituminous Roads: An Indian Perspective” (A. Das and B. Pandey, Journal of Transportation Engineering, 1999:463–471) presents an equation of the form y = a(l/x1)b(l/x2)c for predicting the number of repetitions for laboratory fatigue failure (y) in terms of the tensile strain at the bottom of the bituminous beam (x1) and the resilient modulus (x2). Transform this equation into a linear model, and express the linear model coefficients in terms of a, b, and c.
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- 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 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_forwardAn article in Concrete Research ("Near Surface Characteristics of Concrete: Intrinsic Permeability," Vol. 41, 1989), presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, Σy = 572, Σ.y = 23,530, x = 43, Ex = 157.42, and xy = 1697.80. Assume that the two variables are related according to the simple linear regression model. Statistical Tables and Charts Part 1 Calculate the least squares estimate of the slope. (Round your answer to 3 decimal places.)arrow_forward
- a) Suppose that the two regressions models below are estimated, Y a+BX+u and Y= a +B'x+y°z+u', Explain under which conditions B= ß*. b) Explain whether in simple regression R²= R? . (use formula to explain)arrow_forwardThe article "Earthmoving Productivity Estimation Using Linear Regression Techniques" (S. Smith, Journal of Construction Engineering and Management, 1999:133–141) presents the following linear model to predict earth-moving productivity (in m3 moved per hour): Productivity = - 297.877 + 84.787x, + 36.806x, + 151.680x, – 0.081x, – 110.517x5 - 0.267.x, – 0.016x,x, +0.107.x,x5 + 0.0009448x,x, – 0.244x;x, where X1 = number of trucks X2 = number of buckets per load X3 = bucket volume, in m³ X4 = haul length, in m X5 = match factor (ratio of hauling capacity to loading capacity) X6 = truck travel time, in s If the bucket volume increases by 1 m², while other independent variables are unchanged, can you determine the change in the predicted productivity? If so, determine it. If not, state what other information you would need to determine it. b. If the haul length increases by 1 m, can you determine the change in the predicted productivity? If so, determine it. If not, state what other…arrow_forwardHow can we make predictions using a fitted model in R?arrow_forward
- An economist wants to quantify the offect of olectricity prices on the real economy. By using quarterly data, ho estimated an FDL model over 1950:01 - 200304 and obtained the following result: Ý = 1.2-0.007E, -0.014E,-0.019E, 2-0.024E, 3-0.038E, -0.013E, 0.006E,-0.009E, +0.006E, where Y, is the quartorly percontage change in GDP (i.e. = 100ln(GDP/GDP.) and GDP, denotes the value of quartorly gross domestic product in an economy.). E, is the percentage point difference between electricity prices at date t and thoir maximum value during the past 5 years Suppose that eloctricity prices jump 27% above their previous peak value and stay at this new higher lovel (so that E, 27 and E En2 - 0). Calculate the prodicted (percentage point) offect on output growth for each quartor over the noxt 2 yoars. (Round your responses to two decimal places.) The immediate effect on output in the current period is percent. percent percent percent After 1 quarter - After 2 quarter After 3 quarterarrow_forwardb) What are the three models proposed as extensions of the GARCH model? Describe their advantages over the GARCH.arrow_forward4arrow_forward
- 8-56. + An article in the Australian Journal of Agricultural Research [“Non-Starch Polysaccharides and Broiler Perfor- mance on Diets Containing Soyabean Meal as the Sole Protein Concentrate" (1993, Vol. 44(8), pp. 1483–1499)] determined that the essential amino acid (Lysine) composition level of soy- bean meals is as shown here (g/kg): 22.2 24.7 20.9 26.0 27.0 24.8 26.5 23.8 25.6 23.9 (a) Construct a 99% two-sided confidence interval for o. (b) Calculate a 99% lower confidence bound for o. (c) Calculate a 90% lower confidence bound for o. (d) Compare the intervals that you have computed.arrow_forward2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231arrow_forwardShow the roadmap of how to model the data according i) to whether it is stationary or non-stationary, and of whether the data is cointegrated or not cointegrated. ii) Show cointegration graphically.arrow_forward
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