1.1 Consider a time series process given by (1-B)x, = (1-0,B)z,, where the sequence {z, is a whitenoise with mean zero and variance o. Determine the first four y/ weights of process x, if an ARMA(1,1) model fitted to the data gave₁=0.8 and 0₁ = 0.341.2QUESTION 1Consider an AR (2) model: x - x == $, (x,_₁ − x)+ $₂(x₁_2 − x)+ z,, where z, ~ wn(0,0²).= P(1 - ) (P₂ - P³²)and =1-A²1-A²Show thatusing LSE method.

Step No: 1 1.1 In time series analysis, the autoregressive moving average (ARMA) model…

Answered: process given by (1 − B)x, = (1 – 0,B)=…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q1-Q5: a) Find the value of the line ar correlation coefficient r b) Find the critical values ofr from table A-6 using x= 0.05 c) Determine whether there is sufficient evidence to support a claim of a linear correlation Between the two variables. d) Find the regression equation, e) Letting the first variable be the predietor (x) variable, find the indicated predieted value. Q1. Altitude and Temperature: Altitude 3 10 14 22 28 31 33 ( thousands of feet) Temperature ( °F) 57 37 24 -5 -30 -41 -54 At 6.327 thousand feet, the author recorded the temperature. Find the best predieted temperature at that altitude. How does the result compare to the actual recorded value of 48°F?
8- Conduct residual analysis for the best fitted model. Comment on the normality assumption and constant error variances . Comment on this 4 graph on the the normality assumption and constant error variances
Q3.) In an experiment, the following reading were recorded: Xi Yi 3.6 9.3 4.8 10.2 7.2 11.5 T 6.9 12 10.7 18.6 6.1 13.2 7.9 10.8 9.5 22.7 5.4 12.7 1- Derive the normalized equations for this reading if (y = a + bx) by LSA method. 2- Determine the best fitting of reading (theoretical values of y). 3- Estimate the value of y at x=2.5 Note: In solution of this question, approximate to three decimal digits (at maximum) only after the point.
ou run a regression analysis on a bivariate set of data (n=20n=20). With ¯x=44.9x¯=44.9 and ¯y=42.7y¯=42.7, you obtain the regression equationy=3.921x+57.242y=3.921x+57.242with a correlation coefficient of r=0.264r=0.264. You want to predict what value (on average) for the response variable will be obtained from a value of 140 as the explanatory variable.What is the predicted response value?y = (Report answer accurate to one decimal place.)
The following is a list of 14 measurements. - 13, -6, -45, 53, -3, 83, –23, 79, – 17, -96, – 18, 91, 53, – 13 Send data to calculator Send data to Excel Suppose that these 14 measurements are respectively labeled x,, x,, ..., x: (Thus, -13 is labeled x,, -6 is labeled x,, and so on.) Compute the following. 14 Σ 29х, i = 1
4. Question Draw and upload two datasets that have the same correlation coefficients but different slopes. Use the graphs below as a template for your submission. * (Sext |0, 0.5, Y'I, ext(0.5, e, x'}1 * (Pext10, 0.5. Y'i, Text(0.5. o, x') 1.0 1.0 0.8 - 0.8 0.6 0.6 0.4 - 0.4 0.2- 0.2 0.0 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 plot of chunk cor_slope
There is a relationship between the following variables as y = 1 / (a * x ^ b) (x ^ b: means x over b). a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation. x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10 x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10
12:08 AT&T * 4 all 65% 3. RT = 22 and US = 18 VT = R UV = RS = ST = U II
16.17 In an experiment comparing four diets (treatments), the weight gain y (pounds per day) of pigs was recorded along with two covariates, initial age x₁ (days) and initial weight x2 (pounds). The data are presented in Table 16.11. (a) Using (16.67), (16.68), and (16.69), find Ex, exy, and eyy. Find B. (b) Using (16.77), (16.81), and (16.82), find SSEyr, SST.x, and SS(alu, B). Then test Ho: a₁ = ₂ = a3 = a4, adjusted for the covariates, using the F statistic in (16.83). (c) Test Ho: B = 0 using (16.84). (d) Find B₁, B₂, B3, and 4 using (16.88). Find SSE(F), and SSE(R)y.x using (16.86) and (16.87). Test Ho: B₁ B₂ B3 B4 using (16.89). X1 X2 y X1 78 61 1.40 78 90 59 1.79 99 94 76 1.72 80 71 50 1.47 75 1.26 94 1.28 91 1.34 75 1.55 63 1.57 62 1.26 TABLE 16.11 Initial Age x₁, Initial Weight x2, and Rate of Gain y of 40 Pigs Treatment 1. Treatment 2 Treatment 3 Treatment 4 99 61 80 54 83 57 75 45 62 41 67 40 X2 y X1 74 1.61 78 75 1.31 83 64 1.12 79 48 1.35 70 1.29 85 1.24 83 1.29 1.43 1.29…
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 132 millimeters, and a variance of 64. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would be greater than 128.2 millimeters? Round your answer to four decimal places. Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts Tables
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
An engineer measures the peak current (in microamps) when a solution containing an amount of nickel (in parts per 10°) is added to a buffer. The experiment was repeated for eleven different values of nickel solutions. A scatterplot showing the data is given below: Peak Current in Eleven Buffers with Added Nickel Solutio 60 120 140 100 Amount of nickel (pp million) Suppose a regression line was added to the plot above. If an additional measurement had been taken with the nickel of 62 parts per 10 and a peak current of 0.38 microamps, adding this observation would: O A. increase the intercept, decrease the slope. OB. increase the intercept, increase the slope. C. decrease the intercept, increase the slope. OD. decrease the intercept, decrease the slope. E. not affect the regression line.

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process given by (1 − B)x, = (1 – 0,B)= nd variance o. Determine the first fo data gave =0.8 and 9 = 0.34 model: x₁ - x = (x₁_,₁ − x) + ₂(x₂₁_₂ − x). (ô₂ – ô²) 1-A² - P₂) A and = 2 using LSE me