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7) Consider the intercept-only logistic regression model iBinomial (ni, p) i= 1,...,n yi independent log 1-p...
Consider the zero intercept model given by Yi = B1Xi + ei (i=1,…,n) with the ei normal, independent, with variance sigma^2. For this mode (i) find the sum of (Yi –Yi-hat). (ii) find the sum of (Yi – Yi-hat)Xi. (iii) find the estimator of the error variance, sigma^2. (iv) is the estimator of the error variance biased?
2. Consider a simple linear regression model for a response variable Yi, a single predictor variable ri, i-1,... , n, and having Gaussian (i.e. normally distributed) errors Ý,-BzitEj, Ejį.i.d. N(0, σ2) This model is often called "regression through the origin" since E(Yi) 0 if xi 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function. (Hint: The function...
Consider the least-squares residuals ei-yi-yi, 1, 2, . . . , linear regression model. Find the variance of the residuals Var(e). Is the vari- ance of the residuals a constant? Discuss. n,from the simple
Really short question! Please help me to solve, thank you! (10%)Q3 (Logistic regression): We collected n 15 independent binary observations : i- 1, , 15) and their corresponding covariates {xi : і = 1, , 15). Assume the relationship between yi and zi (for i = 1, , 15) is Vi ~ Bernoulli(p.) and logit(Pi)-α+82i, where logit(t) = log ti. Please 1) write down the likelihood function L(a, B|x, y) of the logistic regression model; 2) derive the Newton method...
1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model using the OLS estimator. (a) Present and discuss assumptions for the OLS estimation.
Consider the linear regression model Yi = β0 + β1 Xi + ui Yi is the ______________, the ______________ or simply the ______________. Xi is the ______________, the ______________ or simply the ______________. is the population regression line, or the population regression function. There are two ______________ in the function (β0 & β1 ). β0 is is the ______________ of the population regression line; β1is is the ______________ of the population regression line; and ui is the ______________. A. Coefficients...
1. Consider a GLM (generalised linear model) for a Poisson random sample Y1,. .. , Y, with \Vi each Yi having a pdf or pmf f(y; A;) = i= 1, . .. ,n. Yi = 0, 1,2, -..; ^; > 0; Y;! Note that the pdf from an exponential family has the following general form b(0) + c(y, a(o) y0 exp f(y; 0, 6) = Suppose the linear predictor of the GLM is n = a+Bxi, with (a,B) being the...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
Logistic Regression In class, we discussed the logistic regression model for binary classification problem. Here, we consider an alternative model. We have a training set {<n, yn) }n where E RD+1 and yn e {0,1}. Like in logistic regression, we will construct a probabilistic model for the probability that yn belongs to class 0 or 1, given en and the model parameters, 0, and 0 (0o,0, ERD+1). More specifically, we model the target Un as: p(yn = 0[xn;00,0) = Cella...
D Question 3 1 pts Consider a logistic regression model where p represents the probability of a successful trial, fitted using the following code: fit <- gim(cbindly, n-y) - , family - "binomial) Which of the following statements is TRUE? explp/(1-p)) is a linear combination of the explanatory terms. loglp/(1-p)) is a linear combination of the explanatory terms. pis a linear combination of the explanatory terms. log(p) is a linear combination of the explanatory terms.