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Problem 2: For logistic regression with 1 predictor variable, the model is specified as E(Y|X=x) 1-E(Y|X=x)...
Problem 1: Consider the model Y = BO + Bi X+e, where e is a N(0,02) random variable independent of X. Let also Y = Bo + B1X. Show that E[(Y - EY)^3 = E[(Ỹ – EY)^3 + E[(Y – Y)1.
For the following logistic regression model, the predictor variable “age” is a quantitative variable. Is there a large difference in the predicted probability of churn when comparing 30-year-old and 40-year-old customers? Yes; the difference of the predicted probability between these age groups is larger than 0.15 (15 percentage points) No; the difference of the predicted probability between these age groups is less than 0.15 (15 percentage points) 5-0.2*Age Predicted probability of churn - 5-0.2*Age Predicted probability of churn -
3. A response variable is related to a predictor variable through the quadratic regression model u yıx(x) = -8.5– 3.2x + 0.7x2 (a) Give the rate of change of the regression function at x = 0, 2, and 3. (b) Express the model in terms of the centered vari- ables as jyjx(x) = Bo + B1(x – ux) + B2(x - ux)2. If ux = 2, give the values of Bo, B1, and B2. (Hint. Match the coefficients of the...
need help with number 2 4.1 Inference For a logistic regression function-parameterized by w and b-with input x E Rm and output y є {-1, +1), the probability ply-Alx) 1 + e (wTxm," 1. Please derive the formulation of p(y =-11x) 2. Please show that p(vlx) 3. Please analyze the decision boundary for this logistic regression classifier. On what condition of x, y will be predicated as +1 or -1? 4.1 Inference For a logistic regression function-parameterized by w and...
Decide (with short explanations) whether the following statements are true or false. e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
Type or pas 2. Let the population regression model between a dependent variable y and an independent variable is given by y= Bo+ B1 x x+ u Suppose that E(u|x) = E(u) = 0 and V(ux) = o2. Based on a random sample ((y, ) i = 1,2,...n) of size n such that (xi- )2>0, let Bo and B be the OLS estimates of Bo and Bi respectively. Answer the following questions (c) Let B i Show that if B1...
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...
6. This problem considers the simple linear regression model, that is, a model with a single covariate r that has a linear relationship with a response y. This simple linear regression model is y = Bo + Bix +, where Bo and Bi are unknown constants, and a random error has normal distribution with mean 0 and unknown variance o' The covariate a is often controlled by data analyst and measured with negligible error, while y is a random variable....
Q6). Suppose that you want to fit two separate regression lines on the same data set - For the first least square fit, Y is the response variable and X is the predictor variable For the second least square fit, X is the response variable and Y is the predictor variable. (a). Show that the product of the slope estimates from the two regression lines is Show that the above two regression lines will never be perpendicular to each other...
2.25 Consider the simple linear regression model y = Bo + B x + E, with E(E) = 0, Var(e) = , and e uncorrelated. a. Show that Cov(Bo, B.) =-TOP/Sr. b. Show that Cov(5, B2)=0. in very short simple way