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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02The following Table summarizes the main estimation results for the below model: C- Bo + B,R + Balet E.where (C) denotes total household Consumption in SL, (R) is the national Incorme, and (1) denotes the Taxes collected from the private sector. The time span goes from 1974, 1st quarter, to 2010, 4th quarter and all the variables are expressed in million Rupees. Dependent variable C Constant R. Coefficient Sd. Eror t-statisties 128 40 3.2 0.90 0.48 0.67 6.0 32 0.15 0.15 R squared Residual Std. 1.35 Deviation Given the information in above table and the null that the Given the information in above table and the null that the Taxes collected from the private sector (B2) is not equal to zero, O a. There is not enough information to test this hypothesis. O b. The test statistic can be computed and the null is rejected in favor of the alternative hypothesis with a 5% significance. O . None cof the these O d. The test statistic can be computed and the null is not rejected in favor of the…Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.
- Let X ~N(0, e2). Find the CRLB for variances of the unbiased estimator of T(0) = 0². %3DSay we have a single response variable Y, and two explanatory variables, X and W. We fit a model as follows: Y = Bo + B1X + B2W + eLet Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s2is known. Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix.
- Consider independent observations y₁, ..., yn from the model Y;~ Poisson(μ). Using likelihood L(μ) and log-likelihood (μ) as appropriate, compute the following items. 1. Derive the maximum likelihood estimate û.Q3. Find out the regression coefficients of Y on X and of x on Y on the basis of following data: Ex = 50, X = 5, EY = 60, Y = 6, EXY = 350 Variance of X= 4, Variance of Y= 9Q. 25 If a Poisson variate X is such that P (x = 1) = P(x=2), Work out P (x = 4).
- Consider a random sample from NB(r, p) where the parameter r is known to be 3. An experiment is run with n = 10 trials and the sample mean is observed to be x̄ = 0.6. (a) Derive a formula for the MLE p̂ as a function of n, r and X̄ . (b) Find the estimate of p. (c) Find the MLE for the population mean.If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.This is Least squares estimates for the one-way ANOVA model. The normal equations for the effects model are as below. Prove in detail how this model was derived. (Hint: Set normal equation first and take a derivative with regard to mu (µ) and tau(τ) respectively.)
