Numerical Analysis
10th Edition
ISBN: 9781305253667
Author: Richard L. Burden, J. Douglas Faires, Annette M. Burden
Publisher: Cengage Learning
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Chapter 3.5, Problem 13ES
To determine
The value
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Two functions ƒ and g are defined in the figure below.
g
6
6
7
8
8
8
9
Domain of f
Range of f
Domain of g
Range of g
Find the domain and range of the composition g.f. Write your answers in set
notation.
(a) Domain of gof:
(b)
Range of gof: ☐
☑
0,0,...
The table below shows the estimated effects for a logistic regression model with squamous cell esophageal cancer (Y = 1, yes; Y = 0, no) as the response. Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcohoic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites.
Variable
Effect (β)
P-value
Intercept
-7.00
<0.01
Alcohol use
0.10
0.03
Smoking
1.20
<0.01
Race
0.30
0.02
Race × smoking
0.20
0.04
Write-out the prediction equation (i.e., the logistic regression model) when R = 0 and again when R = 1. Find the fitted Y S conditional odds ratio in each case.
Next, write-out the logistic regression model when S = 0 and again when S = 1. Find the fitted Y R conditional odds ratio in each case.
The chi-squared goodness-of-fit test can be used to test if data comes from a specific continuous distribution by binning the data to make it
categorical.
Using the OpenIntro Statistics county_complete dataset, test the hypothesis that the persons_per_household 2019 values come from a normal
distribution with mean and standard deviation equal to that variable's mean and standard deviation. Use signficance level a = 0.01.
In your solution you should
1. Formulate the hypotheses
2. Fill in this table
Range
(-⁰⁰, 2.34]
(2.34, 2.81]
(2.81, 3.27]
(3.27,00)
Observed
802
Expected
854.2
The first row has been filled in. That should give you a hint for how to calculate the expected frequencies. Remember that the expected
frequencies are calculated under the assumption that the null hypothesis is true.
FYI, the bounderies for each range were obtained using JASP's drag-and-drop cut function with 8 levels. Then some of the groups were
merged.
3. Check any conditions required by the chi-squared…
Chapter 3 Solutions
Numerical Analysis
Ch. 3.1 - For the given functions f(x), let x0 = 0, x1 =...Ch. 3.1 - Use Theorem 3.3 to find an error bound for the...Ch. 3.1 - Prob. 4ESCh. 3.1 - The data for Exercise 6 were generated using the...Ch. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ESCh. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 17ES
Ch. 3.1 - It is suspected that the high amounts of tannin in...Ch. 3.1 - Prob. 21ESCh. 3.1 - Prove Taylors Theorem 1.14 by following the...Ch. 3.1 - Prob. 1DQCh. 3.1 - If we decide to increase the degree of the...Ch. 3.2 - Let P3(x) be the interpolating polynomial for the...Ch. 3.2 - Nevilles method is used to approximate f(0.4),...Ch. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Suppose xj = j, for j = 0, 1, 2, 3, and it is...Ch. 3.2 - Nevilles Algorithm is used to approximate f(0)...Ch. 3.2 - Prob. 11ESCh. 3.2 - Prob. 13ESCh. 3.2 - Can Nevilles method be used to obtain the...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use Eq. (3.10) or Algorithm 3.2 to construct...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton forward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - Use the Newton backward-difference formula to...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Use Algorithm 3.2 to construct the...Ch. 3.3 - a. Approximate f(0.05) using the following data...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The following data are given for a polynomial P(x)...Ch. 3.3 - The Newton forward-difference formula is used to...Ch. 3.3 - Prob. 14ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Show that the polynomial interpolating the...Ch. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Compare and contrast the various...Ch. 3.3 - Is it easier to add a new data pair using...Ch. 3.3 - Prob. 3DQCh. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - Use Theorem 3.9 or Algorithm 3.3 to construct an...Ch. 3.4 - The data in Exercise 1 were generated using the...Ch. 3.4 - The data in Exercise 2 were generated using the...Ch. 3.4 - Let f (x) = 3xex e2x. a. Approximate f (1.03) by...Ch. 3.4 - The following table lists data for the function...Ch. 3.4 - a. Show that H2n + 1 (x) is the unique polynomial...Ch. 3.4 - Prob. 1DQCh. 3.4 - Prob. 2DQCh. 3.4 - Prob. 3DQCh. 3.5 - Determine the natural cubic spline S that...Ch. 3.5 - Determine the clamped cubic spline s that...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Prob. 6ESCh. 3.5 - Prob. 8ESCh. 3.5 - Prob. 11ESCh. 3.5 - Prob. 12ESCh. 3.5 - Prob. 13ESCh. 3.5 - Prob. 14ESCh. 3.5 - Given the partition x0 = 0, x1 = 0.05, and x2 =...Ch. 3.5 - Prob. 16ESCh. 3.5 - Prob. 21ESCh. 3.5 - Prob. 22ESCh. 3.5 - Prob. 23ESCh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.5 - Prob. 29ESCh. 3.5 - Prob. 30ESCh. 3.5 - Prob. 31ESCh. 3.5 - Prob. 32ESCh. 3.5 - Let f C2[a, b] and let the nodes a = x0 x1 xn...Ch. 3.5 - Prob. 34ESCh. 3.5 - Prob. 35ESCh. 3.6 - Let (x0, y0) = (0,0) and (x1, y1) = (5, 2) be the...Ch. 3.6 - Prob. 2ESCh. 3.6 - Prob. 5ESCh. 3.6 - Prob. 1DQ
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