41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
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- Need help with (d) part. Thank you. statistical program is recommended. Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density,"† was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate Std. Error t value Pr(>|t|) (Intercept) 4.858691 0.059768 81.283 <2e-16 AirVoid −0.074676 0.009923 −7.526 1.21e-06 Residual standard error: 0.03551 on 16 DF Multiple…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.A statistical program is recommended. Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density,"† was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate Std. Error t value Pr(>|t|) (Intercept) 4.858691 0.059768 81.283 <2e-16 AirVoid −0.074676 0.009923 −7.526 1.21e-06 Residual standard error: 0.03551 on 16 DF Multiple R-squared: 0.7797, Adjusted…
- An environmentalist monitored the water quality of a river in city Xby measuring the conductivity of the river monthly. The conductivity of a water body is an early indicator of the water quality. Owing to implementation of activities which were harmful to the nature such as an oil spill, the conductivity in µS/cm of the river decreased. However, a continuous cleaning up plan had been carried out for the river from January until April 2020 and the conductivity measurement for the months had improved as follows: a1, a2, a3, a4, a5…, an 3, 12, 27, 48, 75, …., an 1. Let an represents the conductivity for nmonths since January 2020. By using n in the formula, determine the formula to represent the conductivity sequence, an. 2.What is the estimated conductivity for January 2021? 3. By assuming bn-1= an - an-1, the monthly improvement of conductivity can be represented by the following sequence. Based on the given sequence, determine bn. b1, b2, b3, b4, …, bn = (12-3), (27-12), (48-27),…In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the following table. X1 X2 y 32 20.0 28 39 23.0 28 20 12.8 32 21 16.0 29 25 10.2 31 20 11.6 28 32 17.6 25 29 17.8 28 27 16.0 29 43 26.2 27 22 9.6 32 22 15.2 32 18 8.8 43 32 20.4 24 22 12.2 36 25 14.6 36 25 10.4 29 20 11.6 30 20 12.6 31 24 16.2 36 18 9.2 34 28 16.8 30 a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. d. Which of the models in parts (a) through (c) is the best of the three? Why do you think %3D + E. so?Accumulation of mercury (Hg) in fish is hypothesized to correlate with the fish size. Barbonymus schwanenfeldii is a species commonly found in a dam in Sarawak. Table 1 shows data of Hg concentration (mg/kg) present in three sizes of fish caught in the dam in triplicates. (i, ii, iii was already answered.)
- A worker with a weight of 65 kg and a body surface area of 1.74 , performs physical work activities in several work environments as shown in the following table. The work activities of these workers require energy and a measured metabolic rate of 400 W/m2. During their work activities, the worker wears a coverall made of polyolefin and wears a headgear (1) Calculate the average WBGT of the work environment. (2) Perform an analysis related to the heat stress experienced by the worker, if the worker performs his work activities for 75% of his total working time and the rest is rest, (note: use TLV from ACGIH and ISO 7243)Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density," was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. x 4.35 4.75 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.14 y 4.55 4.49 4.50 4.47 4.48 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.35 4.44 4.40 4.26 4.32 4.34 Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be less than -0.064. Does the sample data support this belief? Carry out a test of appropriate hypotheses using a significance level of 0.05. State the appropriate null and alternative…Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density," was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. x 4.35 4.75 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.14 y 4.55 4.49 4.50 4.47 4.48 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.35 4.44 4.40 4.26 4.32 4.34 (b) Does there appear to be a useful linear relationship between dielectric constant and air void? Carry out a test of appropriate hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses. H0: β1 ≠ 0 vs. HA: β1 = 0 H0: β1 = 0 vs. HA: β1 > 0 H0: β1 = 0 vs. HA: β1 < 0 H0: β1 = 0 vs. HA:…
- Japan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. The article "Innovative Sludge Handling Through Pelletization Thickening"t reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). Consider the following data. 125.4 98.3 201.6 147.2 146.0 124.5 112.3 120.2 161.1 178.8 y 77.9 76.9 81.3 80.0 78.1 78.5 77.4 77.2 79.9 80.4 159.4 145.7 74.9 151.5 144.2 124.8 198.6 132.6 159.6 110.7 79.7 79.2 76.9 78.1 79.6 78.3 81.7 76.8 79.1 78.5 Relevant summary quantities are X; = 2817.4 Fy, = 1575.5, 5x? = 415,815.84, Fxy, = 222,698.08, Fy? = 124,149.53. Also, x = 140.870, y = 78.78, Sy = 18,928.7020, Sy = 757.395, and SSE = 9.222. The estimated standard deviation is o = 0.716 and the equation of the least squares line is…Need 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…Accumulation of mercury (Hg) in fish is hypothesized to correlate with the fish size. Barbonymus schwanenfeldii is a species commonly found in a dam in Sarawak. Table 1 shows data of Hg concentration (mg/kg) present in three sizes of fish caught in the dam in triplicates.