If(x,,y; ).(x,, y; ),..(x,,y«) be a random sample taken from a logistic regression, thenthe log-likelihood cquation is,a),In|Eln(1-z,)-T,b)Σh(1 -π)Σy n-Σh(π)1-7,c)i-11-1d)Σyn(1- r)+Σ -

It is given that (x1, y1), (x2, y2), (x3, y4) … (xn, yn) are the random sample that is taken from a…

Answered: If(x,,y; ).(x,, y; ),..(x,,y«) be a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the data (1,3), (2,5), (3,9.67) (a) Derive the normal equations for the best fit of the form f(x) = - - + Dx? (b) Find C, D using the normal equations derived above and given data. (c) Find a suitable Linearization for f (x) =- + Dx² (Don't find C, D)
For two variables X and Y, we have two regression lines 2X-7Y+3=0 and aX+bY+6=0 for some constants a and b. Suppose we know that X = 2 and Y = 1. Also the second regression line passes through (4, 5). Find the correlation coefficient of these two lines.
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 4), (3, 6), (5, 11), (7, 15), (11, 23)}
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
True or False: For an exponentially distributed random variable, x, P(x) = 1/(b - a).
Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?
When we fit a logistic regression model with a single explanatory term, x, we often assume that logit (pi) Bo + ₁x₂ where, for the ith observation, p; is the probability of a trial being successful and *; is the value of the explanatory variable. Which of the following is a good reason for using the logit link function? We can't use more than one explanatory term unless we use this link function. It allows us to model nonconstant variance in the response variable. It ensures that the probability of success is between 0 and 1. It ensures that the variance of the response is the same for all observations.
Consider the logit regression log(odds(QualExam)) = B, + B, * ParEduc + B2 + Awards, where QualExam is a binary variable that indicates passing the exam if equal to 1, and failing the exam if 0, ParEduc indicates the parents' education level, and Awards is a binary variable that indicates having experience of obtaining award(s) if equal to 1, and not having experience if 0. Given the parents' average education level unchanged, the odds ratio is expected to be for an individual with awards to pass the exam comparing to those without awards. For an individual without awards and the parents' education level of 4, the estimated probability of passing the exam is approximately_. Intercept ParEduc Awards -10.53 2.98 0.48 O A. 1.616; 4%. O B. 1.616; 80%. O C. 0.48; 4%. O D. 0.48; 80%.
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

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If(x,,y; ).(x,, y; ),..(x,,y«) be a random sample taken from a logistic regression, then the log-likelihood cquation is, a) ,In| Eln(1-z,) -T, b) Σh(1 -π) Σy n -Σh(π) 1-7, c) i-1 1-1 d) Σyn(1- r)+Σ -