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- Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (8, 10), (9, 11), (16, 20), (12, 2); y = 2x − 8When the parameter and the sample size is equal to the parameter is being estimated, then the estimator is said to be _________________. a. Unbiased b. Consistent c. Regular d. EfficientUse the standard error to construct the approximate prediction interval for Y using an alpha of 5%.
- Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?Let X1, . . ., Xn be a random sample of componentlifetimes from an exponential distribution withparameter l. Use the factorization theorem toshow that ∑Xi is a sufficient statistic for l.If X1 and X2 constitute a random sample of size n = 2from a Poisson population, show that the mean of thesample is a sufficient estimator of the parameter λ.