Theorem. Any standard deviation of order 'p' may be expressed in terms of a standard deviation of order (p- 1) and a partial correlation coefficient of order (p – 1).
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- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.(d) Does a linear relation exist between the speed at which a ball is hit and the distance the ball travels? The variables speed at which the ball is hit and the distance the ball travels are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value ( ) (Round to three decimal places as needed.)In a p-variate distribution, all the total (order zero) correlation coefficients are equal to P*0. Let P, demote the partial correlation coefficient of order k and R, be the multiple correlation coefficient of one variate on k other variates Prove that k po² 1 (1)A-A-1 =-PxPx-1 1+ (k-1) po and (iii) R2
- Two independent samples have 28 and 19 pairs of observations with correlation co efficients 0.55 and 0.75 respectively. Are these values of r consistent with the hypothesis that both the samples are drawn from the same population?Find the PSD of a stationary random process for which Auto correlation is Rx (t)= 6- e altiIn N(5,4): Round Z-scores to 2 places after the decimal and use rounded value to find the data value in N(5,4). If P(X a) = .02, then the z-score for a = If P(bTwo real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1Suppose that given a particular dataset of (x, y) pairs, the correlation coef- ficient (r) of the least-squares line is -.98. What conclusion can we draw from this 19. information? A. X and Y have a strong linear correlation B. X and Y have a moderate linear correlation C. X and Y have a weak linear correlation D. X and Y are not linearly correlated E. None of the above 20. Given the following summary data from a sample of size 9, what is the slope of the least-squares line for x and y? E; = 24 Σ-70.50 Σ- - 902.25 Ev = 11, 626.75 Yi = 312.5 %3D A. .089 В. 13.150 C. 13.052 D. 10.603 E. None of the aboveCompute co-efficient of correlation from the following given results: x =10, Edx = 0. Edy = 0, E(x-K)? = 1350, Ety-7}²= 2180 and E(x-X) (y-7) =1590Let B₁ and 3₂ denote the OLS estimators of B₁ and 2 in the regression: yi= Bo + Bixi + B2x₁2 + Ui. Let B₁ denote the OLS estimators of B₁ in the regression Vi = Bo + Bixil + Vi. Let 8₁=1(x₁ - x₁)(X₁2 - X₂) / Σ²-₁(x₁₁ — X₁)². a) ₁ is the OLS estimator of a slope parameter from what regression model? b) Show that 1(Vi-Bo - B₁x₁₁ - B2x₁2) (Xi1 — x₁) = 0. c) Prove that B₁ =B1 + Ổ₁ß2. Explain the situations in which omitting x2 from the model will NOT bias the OLS estimate of B₁.Indicate True or False for the following statements: (a) A random (RP) process is a time varying random variable - True or False (b) A random (RP) process is a randomly chosen function of time - True or False (c) A stationary RP depends on time - True or False (d) The mean of a stationary RP depends on time - True or False (e) The autocorrelation of a stationary RP depends on time – True or False (f) The PSD of a WSS random process is always nonnegative and even – True or False (g) White noise is realizable in practice – True or FalseWe can combine the autoregressive model with the moving average model to form an ARMA model. Here is an example. Suppose uz is stationary with mean zero, e is mean zero, variance o, and each draw is iid. Suppose we have serial correlation so that: Ut = pUt_1 + et + Oe,-1 a. Find the cov (ut, et) as function of the parameters and o. b. Find the cov (ut, ut-1) as a function of the parameters, o and o. c. Find the var(ut) as a function of the parameters and o̟. d. Now find cov(ut, ut-1) again, but this time write it as only a function of the parameters and o?.SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning