(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,) = 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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- 1) What is the slope(b1) and what is its statistical interpretation? 2) Perform the test of hypothesis (t-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 3) Perform the test of hypothesis (F-test) on the following and state your statistical decision. Use α = 0.01. Please show all the relevant calculations. H0: β1 = 0 H1: β1 ≠ 0 4) What is the coefficient of determination (r2) i.e., percentage of variability in the monthly rent explained by the independent variable rental property area? Please show all the relevant calculations. 5) What is the 99% confidence interval for the population slope(β1)? Please show all the relevant calculations.?For the model is of the form E(Y) = Bo +B,x,which of the following is true about the variability in the confidence interval of E(Y) and the prediction interval for a single future value of Y when a. There is more variability in the prediction interval of a single value of y than in the confidence interval of E(Y) b. There is less variability in the prediction interval of a single value of y than in the confidence interval of E(Y) c. There is no conclusive statement about the variability between the the two intervals. d. The two intervals always have equal variability1) The population regression function for the 2-variable model is Y,= B, + B,X, +U, Where Ui is used as a surrogate for all the variables omitted from the regression but collectively effect Y₁, why then not use a multiple regression with all the necessary variables included?
- Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 190 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.53 cm, y 81.32 kg, r 0.259, P-value 0.009, and y = 106+ 1.09x. Find the best predicted value of y (weight) given an adult male who is 181 cm tall. Use a 0.10 significance lev. The best predicted value of y for an adult male who is 181 cm tall is kg. (Round to two decimal places as needed.)Let X₁,..., Xn be a random sample from a distribution with one of two pdfs. If 0 = 1, then f(x;0=1) = 1 (0 < x < 1). If 0 = 2, then f(x;0= 2) = 2x1 (0 < x < 1). (a) Give a general form of the MLE of 0. (b) You are given a sample data of 3 values: 0.4, 0.5, 0.8. Find the MLE estimate of 0 based on the data.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-
- Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?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.)
- Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…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.)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.