Suppose a time series Yt is given by a random walk Zt and a white noise process Et where Yt = Zt+Et. Find Ps the coefficients of correlation for Yt.
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- Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let bj and b2 be the estimators for B1 and B2 and recall Eê, where ê; = Y; – bị – b2X;. Suppose the sample correlation between {X; }"_-1 and {Y;}"_, is 0.5 and E(Y; – Ỹ„)² = 100. What is ổ?? %3D n-2 Hint: (i) for simple regression, the regression R? is equal to the squared sample correlation between X and Y. (ii) R² = 1 – SSE where SSE = Eế and SST SST = O a. 7.5 O b. 8.5 О с. 9 O d. 10 O e. 8 O f. 7 Clear my choiceWe 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?.Identify the two procedures that can be used to compute the Spearman correlation.
- I have transportation data with a year variable, categorical and continuous variables. I tried to create a cross section by concatenating all the categorical variables together then regress on the continuous variables with revenue as my dependent variable using Pooled OLS. Unfortunately, i have serial correlation in my model and i am not able to remove the serial correlation. Alternatively, i was thinking of looking at just one year of data or treating the data as a single cross section, including year dummy variables and selecting specific categorical variables as additional dummy variables to determine the effect on revenue. Any issues with that approach or alternative recommendations? Also, its worth noting that i had to remove 15% of my data to ensure each cross section that i created had a year from 2011-2017 to allow me to run the proc panel in SAS.Consider observations (Yit, Xit) from the linear panel data model Yit = Xitβ1 + αi + + λit + ui, where t = 1,...,T ; i = 1,...,n; and αi + λit is an unobserved entity-specific time trend. How would you estimate β1?Suppose that we have two independent data sets from the same process. One was collected in the past and another was collected recently. The observations are: {(r;; Yi), i = 1, n1} and {(r;, Yi), i = n1 + 1, .. , n1 + n2}. The two models are postulated to be 2. Yi ao + a1x; + Ei, i = 1, . . , n1, %3D = Bo + B1x; + Ei; i = n1 +1,,n, where n = nị + n2. a) Express these separate models as a single model in matrix form. b) Find A and c for testing Ho : a1 =
- Expression levels of GeneA and GeneB were measured in 10 cell lines. The researcher would liketo know if expression levels of GeneA and GeneB are related.a. Use a parametric method to test if GeneA and GeneB are correlated.b. Use a non-parametric method to test if GeneA and GeneB are correlated. Carry out all above tests for α = 0.05.Please solve manually not using software program .A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n = 10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all. The dependent variable is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. (Hint: start with the df column). Source SS df MS Between ___ ___ 15 F = 7.50 Within ___ ___ ___ Total ___ ___Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.