Suppose n numbers ave vandoml Selected without vepacement hom a set ot N numbers, that is,...
Suppose that there are six x-variables in a model to predict y. The sample size is n = 100. SSTO = 5000 and SSE = 2250. (a) Calculate R2adj. (Remember that p is the number of regression parameters including the intercept!) (b) Calculate the AICp and BICp values for this model. (c) Suppose that the six x-variables in the model were selected from a set of 10 possible x-variables and that the SSE for a model that contains all 10...
Suppose that Case i is an outlier in the sense that an amount δ is added to its expected value. Let u i be the unit vector with 1 in the ith position and zeros elsewhere and write the revised model is y = Xβ + δu i + e. Weisberg (1985) calls this the mean shift outlier model. Using standard methodology, develop the test statistic for the hypothesis, H 0 : δ = 0 and show that the resulting...
i need help with 2b please is a set of input values, Y- 2. In this question, we reuse the notation of lecture 37: X-{xi, ,x , m-1) is a set of hash values, and H is an [X → Y)-valued random variable {0.1, In lecture, we showed that for any hash value y e Y, the expected number of input values that hash to y is k/m, where k XI and m Yl. However, in determining the time it...
Suppose that Case i is an outlier in the sense that an amount 8 is added to its expected value. Let ui be the unit vector with 1 in the ith position and zeros elsewhere and write the revised model is Weisberg (1985) calls this the mean shift outlier model. Using standard methodology, develop the test statistic for the hypothesis, Ho: 8 -0 and show that the resulting t-statistic, with n - m- 2 degrees of freedom, is equivalent to...
I need help on this, please help me Suppose that X = (Xi, X2, , Xn) and Y = (Yİ, ½, . . . ,Yn) are randon samples from continuous distributions F and G, respectively. Wilcoxon's two-sample test statistic W W(X,Y) is defined to be Σǐ1+nn 1 R d n+m where Ri is the rank of Yn the combine sample. 2. Show that W can be written as where U is the number of pairs (X,, Y) with X, <...
CLUSTER SAMPLING WITH ESTIMATION Suppose a population of size N is divided into K- N/M groups of size M. We select a sample of size n -km the following way: » First we select k groups out of K groups by simple random sampling . We then select m units in each group selected on the first step by simple random sampling . The estimate of the population mean is the average Y of the sample. Let μί be the...
2. (Continmed from Onestion 2 in Homework 6) The data set cars gives the sneed (X) and stopping distance (Y) for n=50 (very old) statistics cars. Suppose you are given the following summary n ΣΧ- - 770; (Xi-X) 1370; Yi2149; XY 38482 i-1 i-1 i1 i1 In addition, suppose we fit the simple linear regression model Y= iid N(0, a2), and obtain RSS = (Y-Y) OLS for the ith observation. +B1Xi+ 478.02 where Y is the fitted value given by...
linear statistics modeling and regression 2) Suppose you have multiple regression set up Ynxi XnxpBpxi Sxl and f ~ N(0nx1, σ21.). P Po X(X,X)-X, be the projection matrix on the column space of X. a) Show residual vector, e = (1,-P)Y. Here e is the vector of residuals ei S. b) Show that the variance of e, is 1 - Pi, where P is the i, j th entry of the matrix P c) Show that the sample covariance of...
o-8. (15 points) Bob's simple toy RSA eryptosystem has public key kyub(n, e) (65,5), where n =p,-5x13-65 and e-5. I. Describe the key pair generation procedure for Bob to generate his private key kor- d. With the above given parameters, use EEA to calculate d 2. Describe RSA encryption procedure that Alice uses to encrypt her plaintext message x to its above given parameters, what will be y? ciphertext y before sending the message to Bob. Suppose Alice's message x-...
7-10 There is a new lottery game where twelve numbers are chosen from the set of numbers from 1 to 24, with no repeats. One of the ways to win is to match ZERO numbers, the other way to win is to match ALL the numbers. Order does not matter. 7. Calculate the probability of getting all the numbers correct. Show the setup of the numbers, in case calculations go silly and also to show that you didn't just Google...