The following data given are collected from the experimental measurement on the electrical circuit with the current as input variable and voltage as output variable: (b) i 1.2 2.4 3.6 4.8 6. 7.2 v(i) 21a 9la 18la 271a 38la 45la 57la Compare FOUR(4) suitable methods to approximate v'(6) in 4 decimal places in which the exact solution of v'(6) is 8.3878.

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…

1.4 Consider the following two functions: (i) e(v) exp dx V27 V2m. (ii) 9(v) = 2 tan-(v) %3D Explain why both of these functions fit the requirements of a sigmoid function. How do these two functions differ from each other?

Consider the following simple relationship between aggregate savings St and aggregate income Yt: St= a + BYt + εt, t = 1, ..., T. For some country this relationship is estimated by OLS over the years 1956-2005 (T = 50). The results are given below: = Variable Coefficients Constant 38.90 Y 0.098 22.57, R² = 0.93, DW = 0.70 Standard error 4.57 0.009 where ô is the standard error of regression, R² is the multiple correla- tion coefficient, and DW is the Durbin-Watson statistic. (a) Explain why the result indicate that there may be a problem of positive autocorrelation. Can you give arguments why in eco- nomic models positive autocorrelation is more likely than nega- tive one?

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…

Q.21 Given the following set of discrete data: 0.2 1.0832 0.3 0.4 y 1.1972 1.3771 Find the approximate value of f'(0.4) using all the appropriate difference formulas. solution with f(x) = ²x². Which method gives better approximation? Check X 0.4 1.6487 your 0.6 2.0544 0.7 2.6644

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,"t 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. t value 81.283 Estimate Std. Error Pr (>It|) 4.858691 (Intercept) AirVoid 0.059768 F) Airvoid 1 0.071422 0.071422 56.635 1.214e-06 Residuals 16 0.20178 0.001261

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,"t 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 simple linear regression of y on x. Estimate Std. Error t value Pr (>|t|) (Intercept) 4.858691 0.059768 81.283 F) Airvoid 1. 0.071422 0.071422 56.635 1.214e-06 Residuals 16 0.20178 0.001261 (a) Obtain the equation of the least squares line. (Enter your numerical values to six…

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Consider the following data set Xị -2 1 3 Yi 2 -1 1 And the model y = ao + a¿Sin(x) In the sense of the least square, which one of the following two choices for the model parameters fits better the data set? 1. ao = -4.1 and a, = -2.7 2. ao = -1.9 and a, = 0.1 Give detailed calculations.