To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials with respect to evaluation at the points t= -5,-3,-1, 1, 3, and 5. a. Show that the first three orthogonal polynomials are Po(t) = 1, p₁(t) = 1, and p2(1) = 1²-35 (The polynomial p₂ has been scaled so that its values at the evaluation points are small integers.) b. Fit a quadratic trend function to the data (-5, 1), (-3, 1), (-1,4), (1,4), (3,6). (5.8)
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- Given datasets X: x1 (1, 4), x2 (2, 3), x3 (3, 4), and x4 (5, -3), x5 (6, -1), x6 (7, -1) with label y = (- 1, -1, -1, 1, 1, 1) respectively, find analytically hard margin W and bias b so that you will be able to determine linear discriminant function f(X) = WT . X + b. You may need to draw the points and estimate the boundary decision function that may be used to help you to make a very first guess the parameter W and b. Once you found the correct discriminant function f(X) = WT . X + b, test your function to correctly classify x1 (1, 4) and x4 (5, -3). Please thoroughly describe.The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Test the claim, at the α = 0.05 level of significance, that a linear relation exists between the two variables, Apply classical and p-value approaches. Show step1-step3. Input β1 as "beta1" or "β1". Do NOT input as "b1". Temperature x 72 85 91 94 100 80 90 78 99 number of absences y 3 7 10 10 8 9 4 15 15 Round critical value and test statistic to nearest hundredth. (0.125 would be entered 0.13) Round p-value to nearest ten-thousandth. (0.14275 would be entered 0.1428)A “Cobb–Douglas” production function relates production (Q) to factorsof production, capital (K), labor (L), and raw materials (M), and an errorterm u using the equation Q = λKβ1Lβ2Mβ3eu, where λ, β1, β2, and β3 areproduction parameters. Suppose that you have data on production and thefactors of production from a random sample of firms with the same Cobb–Douglas production function. How would you use regression analysis toestimate the production parameters?
- The data below are the temperatures on randomly chosen days during the summer and the number of employee absences at a local company on those days. Test the claim, at the α = 0.05 level of significance, that a linear relation exists between the two variables, Apply classical and traditional approaches. Show step1-step3. Input β 1 as "beta1" or "β 1". Do not input as "b1". Temperature x 72 85 91 94 100 80 90 78 99 number of absences y 3 7 10 10 8 9 4 15 15A researcher wants to examine the relationship between time spend on social media (variable X) and loneliness (variable Y) in young adults. A randomly sample of n = 52 young adults was asked how much time in average they spend on social media each day and how lonely day feel on a typical day. The partial computations of collected data produced the following results: SP = -14 MX = 10 SSx = 36 MY = 16 SSY = 49 A. Based on these results, is there a significant correlation between time spend on social media and loneliness among young adults? Use a Pearson correlation test with p < .05, 2-tails to answer this research question. Follow the steps of hypothesis testing and insert your answers below. In your calculations,round all numbers to two decimal places to avoid rounding errors. ANSWER H0: H1: Computed Pearson r = df for decision about H0: Critical r-value used for decision about H0: Decision about H0 (i.e., reject or fail to…The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. Year 2010 2012 2014 2016 2018 2020 CO2 Emissions 337.5 361.5 395.1 425.8 451.1 496.4 Year 2022 2024 2026 2028 2030 2032 CO2 Emissions 558.2 592.9 628.7 662.1 709.1 742.7 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.)y(x) = (b) Find the model's estimate for the 2028 data point. (Round your answer to two decimal places.) million metric tons(c) Find the slope of the linear model. (Round your answer to two decimal places.)Interpret the slope of the linear model. For each year since ---Select--- 2009 2010 2015 2028 2032 , carbon dioxide emissions in the U.S. are expected to change by million metric tons.
- 1. Referring to Scenario 13-11, which of the following is the correct interpretation for the slope coefficient?a) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.b) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands.c) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.d) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.Determine whether the following statements are true or false? (a) When interpolating n data points, (x;, y), i = 1,2,..., n, using polynomial interpolation, there are n unknown coefficients to determine. (b) When interpolating n data points, (x;, yi), i = 1,2, ., n, using cubic spline interpolation (not-a-knot spline), there are 4(n - 2) unknown coefficients to determine. (c) When performing linear curve fitting for n data points, (x;, yp), i = 1,2,..., n, there are 2n unknown model parameters to determine. (d) When performing nonlinear curve fitting for n data points, (x;, Vi), i = 1,2. unknown model parameters depend on the model form assumed.Need help with parts d and k. Data: TSERofReturn AcmeRofReturn 1 0.42478 -0.48194 2 1.61213 -0.73284 3 -0.98754 -2.28445 4 -0.30013 -1.55312 5 1.41215 0.68674 6 0.68725 -1.31132 7 0.03733 -0.83295 8 -1.72494 -1.71975 9 0.33729 1.14443 10 -1.07502 -1.79885 11 0.86222 0.89736 12 1.17468 1.66664 13 -0.38761 -0.02658 14 1.66212 0.9086 15 1.09969 1.99935 16 -0.06266 0.46148 17 -1.96241 -1.41004 18 -1.32499 -0.38086 19 -1.51247 -1.90904 20 0.74974 0.91873 21 -0.38761 -0.49714 22 -0.17514 -1.31385 23 -3.41222 -1.15681 24 -0.01266 2.11718 25 0.16231 1.78766 26 -0.82506 1.30344 27 -0.41261 -0.43377 28 0.2623 -1.70274 29 -1.16251 0.4692 30 -1.05003 0.27671 31 -0.65008 -0.63741 32 0.62475 2.9895 33 -0.68758 1.3613 34…
- 23. Compute the actual values indicated by A,B,C and D in that order. A. 2569, 560, 996553, 87103 B. 996553, 2569, 87103, 560 C. 650, 632699, 18730, 9562 D. 2695, 650, 633599, 17830 24. If the general linear regression model is given by the equation: y=a+bx; considering the information obtained in figure 2, compute the value of b. A. 210.185 B. 121.852 C. 21.850 D. 2.185 25. If the general linear regression model is given by the equation: y=a+bx; considering the information obtained in figure 2, compute the value of a. A. 397.210 B. 973.102 C. 210. 379 D. 237.021Find the curve of best-fit y = axb to the following data by using the method of least square.The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number…