QUESTION 33.1 Consider the model yij = i +eij,i = 1,..., a; j = 1, ..., ni.3.1.1 Show that u; is estimable.[32 Marks](7)3.1.2 Find the best linear unbiased estimator (b.l.u.e) of μi.(5)3.2 Consider n serially correlated observations y; from a normal population. This means that:E [yi]=μ and var (yi) = 0²; the correlation coefficient between y; and y₁+1 is p for i =1,, n 1; and that all other correlation coefficients are zero. Show that:3.2.1 E[y]=;-3.2.2 Var ()= [1 + 2p (1 − 1)]; and(5)ཆེསྱེÊ(7)3.2.3 E [S2] = 0² (124), where s² is unbiased estimator of σ².(8)

(3.1)(3.1.1) :yij=μi+eij,where i=1,...,a and j=1,...,nHere, yij is the observed value, μi is…

Answered: QUESTION 3 3.1 Consider the model yij =…

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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4. Question 4: Y is a discrete random variable with PMF S1/3, y=1 p(y) = 2/3, y = 2 (a) Find the MGF for Y. (b) Develop the first two raw moments from MGF and find the variance V(Y). Answers:
1-5. A study is conducted to determine the relationship between a driver’s age and the number of accidents a person has over a one-year period. The data are shown below. At α = 0.05, using Pearson correlation, is there a significant relationship between a driver’s age and the number of accidents a person? 1. What is the value of r? a) -0.172 b) -0.892 c) 0.172 d) 0.892 2.The regression equation is defined by y' = a + bx. What is the value for a? a) 4.02 b) 3.36 c) 3.07 d) 2.86 3. The regression equation is defined by y' = a + bx. What is the value for b? a)0.34 b) 0.29 c) -0.03 d) -0.34 4. If we do t test for the correlation coefficient. What will be the test value? a)1.36 b) 1.28 c) -0.43 d) -0.56 5. What is the critical value to be used in the given problem? a) ±1.943 b) ±2.306 c) ±2.365 d) ±2.447
Q5. (a) For what range of values can the coefficient of correlation of a sample of 52 pairs be considered significantly different from zero at the 1% level of significance? (b) Do the following for the data Days after emergence, X Average dry matter Conventional, Y, Yield (g'plant) Improved, Y2 9. 35 52 170 270 49 50 71 180 91 250 270 3 10 104 Compute the coefficients of correlation between X and Y1, Yi and Y2, and X and Y2 Compute coefficients of determination between X and Y 1, and X and Y2. Interpret these coefficients. ii) iii) Test the hypothesis that the population correlation coefficient between Yi and Y: is 0.80 against the alternative that it is not. |Simple Regression & Correlation]
ol 106. Use the two scenarios presented in Figure 7.12 to answer the following question about the two sources of variability in ANOVA. 3.5 3.0 2.5 2.0 1.5 (i) HA: P₁ P2 ‡ P3 (iii) HA not all proportions are equal to this po 1.0 Figure 7.12: Within vs Between Variability in ANOVA onnisth Scenario A L (d) Recall that, O 2 H 3 2.05 2.10 2.15 2.20 2.25 2.30 2.35 (ii) Ho: M₁ M₂ = μ3 sans are (iv) HA: not all means are equal 720 qeaoluet alt sot mol 4 mobor 2924 (6) 2 3 4 gob za aim onbala (1) di batt (9) w-qodt fonqtotal bac o2 (6) (Troy ote12. (0) (a) Which scenario provides stronger evidence that the difference in factor level means represents true differences in the population means? Explain why in your own words. Scenario B 1 = stogol 05 O 1 oftaltete fest out of sulav gris I (b) Which scenario exhibits more variability within each factor level? Is this measured by SSError or SSFactor? Agulow (c) Which scenario exhibits more variability between each factor level? Is this measured by…
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…
question 12.12 using the numbers from 12.11.
The following results were obtained in a study of correlation coefficient between two variables X and Y : n=50, x =10, o,=3; y O, = 2; r. = 0.3. xy || However, on subsequent verification it was found that one value of X = 10 and one value of Y = 6 were inaccurate and hence weedėd out. With the remaining values how is the original value of correlation coefficient affected.
9.12 For the chemical reaction data of Table 7.4 with dependent variable y2, compute the diagnostic measures ŷi, &i, hii, ri, ti, and Di. Display these in a table similar to Table 9.1. Are there outliers or potentially influential obser- vations? Calculate PRESS and compare to SSE.
Find question 3 using EXCEL
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).

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