You are given:(i)A survival study uses a Cox proportional hazards model with covariates Z, and Z,each taking the value 0 or 1.(ii)The maximum partial likelihood estimate of the coefficient vector is:(B,.B-) = (0.71,0.20)(ii)The baseline survival function at time to is estimated as S(t) = 0.65.Estimate S(t,) for a subject with covariate values Z = Z, =1.(A)0.34(B)0.49(C)0.65(D)0.74(E)0.84

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Answered: You are given: (i) A survival study…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Consider the simple linear regression model Y = a +Bx + E for i = 1,2,...,n. The variances of two estimators i.e. V(@) and V(B) are defined as respectively Nanersite of ARm of Select one: and V(8) +2 (+ %3! V(a) = o? %3D v(a) = o? ; and V(B) = Syx o v(a) = o (:-mnd v(A) - and V(B) = o v(a) = o? (1 + and V(B): Syx = a4 o va) = (; +)md V(f) = and V(ß) Syy %3D Syr fs fo fa 24 & 5 7 V E R Y D T-
Consider the following population linear regression model of individual food expenditure: Y = 50 + 0.5X + u, where Y is weekly food expenditure in dollars, X is the individual’s age, and 50+0.5X is the population regression line. Suppose we generate artificial data for 3 individuals using this model. This artificial sample, which consists of 3 observations, is shown in the following table: Answer the following questions. Show your working. (a) What are the values of V1 and V4? (b) Suppose we know that in this artificial sample, the sample covariance between X and Y is 150, and the sample variance of X is 100. Compute the OLS regression line of the regression of Y on X. (Hint: Assume these summary statistics and the OLS regression line continue to hold in parts (c)-(e).) (c) What are the values of V5 and V7?
Let Y = β0 + β1x + E be the simple linear regression model. What is the interpretation of the least squares estimate for β0? Select one: a. It is an estimate of the expected value of the response variable Y when the explanatory variable X is zero. b. It is an estimate of the change in the expected value of the explanatory variable X for every unit increase in the response variable Y. c. It is an estimate of the change in the expected value of the response variable Y for every unit increase in the explanatory variable X. d. It is an estimate of the expected value of the explanatory variable X when the response variable Y is zero.
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You test some components with a Weibull distribution at temperatures of 100 Celcius and 60 Celcius. At those temperatures you estimate a characteristic life of 15000 hours and 25000 hours respectively. hint: Boltzmann's constant is k = 8.617 x 10-5. Temperature in Celcius + 273.15 = temperature in Kelvin. If n is an integer, T(n) = (n – 1) a) Using linear regression, estimate the Arrhenius model parameters A and AH. b) Give the MTTF, median, and 90th percentile at T = 20 Celcius. Assume that the shape parameter is 0.5
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 189 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.70 cm, y=81.43 kg, r=0.324, P-value=0.001, and y=−101+1.06x. Find the best predicted value of y (weight) given an adult male who is 151 cm tall. Use a 0.10 significance level. Question content area bottom Part 1 The best predicted value of y for an adult male who is 151 cm tall is enter your response here kg. (Round to two decimal places as needed.)
1. Simple Linear Regression Estimation: (а) For the model y; B1 + B2x; + ui, define the fitted value ĝ; and residual û;. (b) x to arrive at estimates for B1 and B2? How does OLS take data on the outcome variable y and the independent variable Suppose you have the OLS estimate of the slope coefficient B2 from regressing ax; is equal to (c) y on x. Show that the slope coefficient if you regressed y on x* for x B2/a, where a is some constant. To be clear, I want you to show that B = B2/a, where B2 is the OLS estimate of B2 from the model Yi = B1 + B2x; + ui, and B is the OLS estimate of B; from the model y; = Bi + B5x + U;.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 188 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.62 cm, y = 81.37 kg, r 0.113, P-value = 0.263, and y = - 105+1.01x. Find the best predicted value of y (weight) given an adult male who is 142 cm tall. Use a 0.05 significance level. %3D The best predicted value of y for an adult male who is 142 cm tall is kg. (Round to two decimal places as needed.)
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Consider the following simple linear regression model, Y; = Po + B₁X₁ + εi, for i=1,2,...,n, where &'s are all independent and normally distributed with E(₁) = 0, and Var(₁) = 0². i) Check whether a statistic Y = Y + B₁ (X₁-X) is an unbiased estimator of the mean of the response variable E(Y) or not. Justify your conclusion.
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