Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
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Chapter 3.4, Problem 11E
To determine
To compute the value of E(Y)
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Suppose that we estimate a logit model based on an intercept and two explanatory variables
A=0.1A=0.3= A=-0.2 and the average value
and the parameter estimates are respectively
₂=0.5,₂=0.8
of the explanatory variables are
In the probability that the outcome corresponding to y = 1 to
Fall by 0.2
Fall by 0.16
Increase by 0.8
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A 1-unit Increase in X3 will cause an increase
Suppose a logistic regression model is fitted for the probability of car ownership for residents
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x2 is gender of the resident of the city (x2=1 for a male and x2=0 for a female resident)
a) Interpret el and e82
b) if BO= -1.6, B1=0.4 and B2=3, estimate the probability of a resident in the city owning a car.
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.
Chapter 3 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
Ch. 3.1 - Show that the mean, variance, and mgf of the...Ch. 3.1 - Let X be a continuous random variable with pdf...Ch. 3.1 - Customers arrive randomly at a bank tellers...Ch. 3.1 - If the mgf of X is M(t)=e5te4tt,t0andM(0)=1,, find...Ch. 3.1 - Let Y have a uniform distribution U(0,1), and let...Ch. 3.1 - A grocery store can order n watermelons from a...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - For each of the following functions, (i) find the...Ch. 3.1 - Prob. 9ECh. 3.1 - The pdf of X is f(x)=cx2,1x. (a) Calculate the...
Ch. 3.1 - The pdf of Y is g(y)=cy3,1y. (a) Calculate the...Ch. 3.1 - Sketch the graphs of the following pdfs and find...Ch. 3.1 - The logistic distribution is associated with the...Ch. 3.1 - Find the variances of each of the distributions...Ch. 3.1 - The life X (in years) of a voltage regulator of a...Ch. 3.1 - Let f(x)=(x+1)2,1x1. Find (a) 0.64, (b) q1=0.25,...Ch. 3.1 - An insurance agent receives a bonus if the loss...Ch. 3.1 - Prob. 18ECh. 3.1 - The total amount of medical claims (in $100000) of...Ch. 3.1 - Nicol (see References) lets the pdf of X be...Ch. 3.1 - Let X1,X2,...,Xk be random variables of the...Ch. 3.2 - Prob. 1ECh. 3.2 - Telephone calls arrive at a doctors office...Ch. 3.2 - Let X have an exponential distribution with mean...Ch. 3.2 - Let F(x) be the cdf of the continuous-type random...Ch. 3.2 - There are times when a shifted exponential model...Ch. 3.2 - A certain type of aluminum screen 2 feet in width...Ch. 3.2 - Find the moment-generating function for the gamma...Ch. 3.2 - If X has a gamma distribution with =4 and =2, find...Ch. 3.2 - If the moment-generating function of a random...Ch. 3.2 - Use the moment-generating function of a gamma...Ch. 3.2 - Let X have a gamma distribution with parameters ...Ch. 3.2 - Let X equal the number of alpha particle emissions...Ch. 3.2 - If X is x2(23), find the following: (a)...Ch. 3.2 - If X is x2(12), find constants a and b such that...Ch. 3.2 - Prob. 15ECh. 3.2 - Cars arrive at a tollbooth at a mean rate of five...Ch. 3.2 - If 15 observations are taken independently from a...Ch. 3.2 - Say the serum cholesterol level (X) of U.S. males...Ch. 3.2 - A bakery sells rolls in units of a dozen. The...Ch. 3.2 - The initial value of an appliance is $700 and its...Ch. 3.2 - A loss (in $100000) due to fire in a building has...Ch. 3.2 - Find the index of skewness of the x2(r)...Ch. 3.2 - Some dental insurance policies cover the insurer...Ch. 3.3 - If Z is N(0,1), find (a) P(0.47Z2.13). (b)...Ch. 3.3 - If Z is N(0,1), find (a) P(0Z0.78). (b) P(2.46Z0)....Ch. 3.3 - If Z is N(0,1), find values of c such that (a)...Ch. 3.3 - Find the values of (a) z0.10, (b) z0.05, (c)...Ch. 3.3 - If X is normally distributed with a mean of 6 and...Ch. 3.3 - If the moment-generating function of X is...Ch. 3.3 - If X is N(650,400), find (a) P(600X660). (b) A...Ch. 3.3 - Prob. 8ECh. 3.3 - Find the distribution of W=X2 when (a) X is...Ch. 3.3 - If X is N(,2) show that Y=aX+b is N(a,+b,a22),a0,...Ch. 3.3 - A candy maker produces mints that have a label...Ch. 3.3 - Prob. 12ECh. 3.3 - The serum zinc level X in micrograms per deciliter...Ch. 3.3 - The strength X of a certain material is such that...Ch. 3.3 - The fill problem is important in many industries,...Ch. 3.3 - The graphs of the moment-generating functions of...Ch. 3.3 - Prob. 17ECh. 3.4 - Let the life W (in years) of the usual family car...Ch. 3.4 - Suppose that the length W of a mans life does...Ch. 3.4 - Let Y1 be the smallest observation of three...Ch. 3.4 - Prob. 4ECh. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Let X be a random variable of the mixed type...Ch. 3.4 - Prob. 7ECh. 3.4 - Find the mean and variance of X if the cdf of X is...Ch. 3.4 - Consider the following game: A fair die is rolled....Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Let X have an exponential distribution with =1;...Ch. 3.4 - A loss X on a car has a mixed distribution with...Ch. 3.4 - A customer buys a $1000 deductible policy on her...Ch. 3.4 - A certain machine has a life X that has an...Ch. 3.4 - Prob. 16ECh. 3.4 - Some banks now compound daily, but report only on...Ch. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Let X be the failure time (in months) of a certain...Ch. 3.4 - In a medical experiment, a rat has been exposed to...
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