Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 12.2, Problem 13E
To determine
To prove: G has a vertex v such that
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Y- ___b=_____ (X- )
For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical)
Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79
5) State any theorems that you use in determining your solution.
a) Suppose you are given a model with two explanatory variables such that:
Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n
Using partial differentiation derive expressions for the intercept and slope
coefficients for the model above.
[25 marks]
b)
A production function is specified as:
Yi = α + B₁x1i + ẞ2x2i + Ui,
i = 1, 2, ... n,
u₁~N(0,σ²)
where:
y = log(output), x₁ = log(labor input), x2 = log(capital input)
The results are as follows:
x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10,
= 8, Syy = 10,
S2y
n = 23 (individual firms)
i) Compute values for the intercept, the slope coefficients and σ².
[20 marks]
ii)
Show that SE (B₁) = 0.102.
[15 marks]
iii)
Test the hypotheses: ẞ1
=
1 and B2 = 0, separately at the 5%
significance level. You may take without calculation that SE (a) = 0.78
and SE (B2) = 0.102
[20 marks]
iv)
Find a 95% confidence interval for the estimate ẞ2.
[20 marks]
Chapter 12 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 12.1 - Prob. 1TFQCh. 12.1 - Prob. 2TFQCh. 12.1 - Prob. 3TFQCh. 12.1 - Prob. 4TFQCh. 12.1 - Prob. 5TFQCh. 12.1 - Prob. 6TFQCh. 12.1 - Prob. 7TFQCh. 12.1 - Prob. 8TFQCh. 12.1 - Prob. 9TFQCh. 12.1 - Prob. 10TFQ
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - 9. The vertices in the graph represent town; the...Ch. 12.1 - Prob. 11ECh. 12.1 - 12. [BB] suppose and are two paths from a vertex...Ch. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - 17. [BB] Recall that a graph is acyclic if it has...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - The answers to exercises marked [BB] can be found...Ch. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - A forest is a graph every component of which is a...Ch. 12.1 - Prob. 27ECh. 12.2 - Prob. 1TFQCh. 12.2 - Prob. 2TFQCh. 12.2 - Prob. 3TFQCh. 12.2 - Prob. 4TFQCh. 12.2 - Prob. 5TFQCh. 12.2 - Prob. 6TFQCh. 12.2 - Prob. 7TFQCh. 12.2 - Prob. 8TFQCh. 12.2 - Prob. 9TFQCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.3 - If Kruskal’s algorithm is applied to after one...Ch. 12.3 - 2. If Kruskal’s algorithm is applied to we might...Ch. 12.3 - 3. If Kruskal’s algorithm is applied to we might...Ch. 12.3 - If Prim’s algorithm is applied to after one...Ch. 12.3 - If Prims algorithm is applied to we might end up...Ch. 12.3 - If Prims algorithm is applied to we might end up...Ch. 12.3 - Prob. 7TFQCh. 12.3 - Prob. 8TFQCh. 12.3 - Prob. 9TFQCh. 12.3 - Prob. 10TFQCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - The answers to exercises marked [BB] can be found...Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - In our discussion of the complexity of Kruskals...Ch. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.4 - The digraph pictured by is a cyclic.Ch. 12.4 - Prob. 2TFQCh. 12.4 - Prob. 3TFQCh. 12.4 - Prob. 4TFQCh. 12.4 - Prob. 5TFQCh. 12.4 - Prob. 6TFQCh. 12.4 - Prob. 7TFQCh. 12.4 - Prob. 8TFQCh. 12.4 - Prob. 9TFQCh. 12.4 - Prob. 10TFQCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - 5. The algorithm described in the proof of...Ch. 12.4 - How many shortest path algorithms can you name?...Ch. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - [BB] Explain how Bellmans algorithm can be...Ch. 12.4 - Prob. 14ECh. 12.5 - Prob. 1TFQCh. 12.5 - Depth-first search has assigned labels 1 and 2 as...Ch. 12.5 - Depth-first search has assigned labels 1 and 2 as...Ch. 12.5 - Prob. 4TFQCh. 12.5 - Prob. 5TFQCh. 12.5 - Prob. 6TFQCh. 12.5 - Prob. 7TFQCh. 12.5 - Prob. 8TFQCh. 12.5 - 9. Breadth-first search (see exercise 10) has...Ch. 12.5 - Prob. 10TFQCh. 12.5 - Prob. 1ECh. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - 4. (a) [BB] Let v be a vertex in a graph G that is...Ch. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - [BB; (a)] Apply a breath-first search to each of...Ch. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.6 - Prob. 1TFQCh. 12.6 - Prob. 2TFQCh. 12.6 - Prob. 3TFQCh. 12.6 - Prob. 4TFQCh. 12.6 - Prob. 5TFQCh. 12.6 - Prob. 6TFQCh. 12.6 - Prob. 7TFQCh. 12.6 - Prob. 8TFQCh. 12.6 - Prob. 9TFQCh. 12.6 - Prob. 10TFQCh. 12.6 - Prob. 1ECh. 12.6 - Prob. 2ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Prob. 12ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - 5. (a) Let G be a graph with the property that...Ch. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - In each of the following graphs, a depth-first...Ch. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RE
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