Mind on Statistics
5th Edition
ISBN: 9781285463186
Author: Jessica M. Utts, Robert F. Heckard
Publisher: Brooks Cole
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Chapter 3, Problem 3.34E
Explain how two variables can have a perfect curved relationship yet have
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Chapter 3 Solutions
Mind on Statistics
Ch. 3 - For each of the following pairs of variables, is...Ch. 3 - For each of the following pairs of variables, is...Ch. 3 - The figure for this exercise is a scatter plot of...Ch. 3 - Prob. 3.4ECh. 3 - Prob. 3.5ECh. 3 - Prob. 3.6ECh. 3 - Prob. 3.7ECh. 3 - Prob. 3.8ECh. 3 - The data in the following table are the geographic...Ch. 3 - Refer to the latitude and temperature data in the...
Ch. 3 - Prob. 3.11ECh. 3 - The following table shows sex, height (inches),...Ch. 3 - Prob. 3.13ECh. 3 - Refer to Exercise 3.13 in which a regression...Ch. 3 - Prob. 3.15ECh. 3 - Prob. 3.16ECh. 3 - The equation for converting a temperature from x =...Ch. 3 - The average August temperatures (y) and geographic...Ch. 3 - A regression equation for y = handspan (cm) and x...Ch. 3 - Imagine a regression line that relates y average...Ch. 3 - Prob. 3.21ECh. 3 - The figure for Exercise 3.8 is a scatterplot of...Ch. 3 - Refer to Exercise 3.22. Predict the pulse rate...Ch. 3 - The average January temperatures (y) and...Ch. 3 - Prob. 3.25ECh. 3 - Prob. 3.26ECh. 3 - Prob. 3.27ECh. 3 - Remember that r2 can be expressed as a proportion...Ch. 3 - Prob. 3.29ECh. 3 - Prob. 3.30ECh. 3 - Prob. 3.31ECh. 3 - Prob. 3.32ECh. 3 - Prob. 3.33ECh. 3 - Explain how two variables can have a perfect...Ch. 3 - Prob. 3.35ECh. 3 - Prob. 3.36ECh. 3 - The figure for this exercise (below) shows four...Ch. 3 - Refer to the figure for the previous exercises. In...Ch. 3 - Prob. 3.39ECh. 3 - Prob. 3.40ECh. 3 - Prob. 3.41ECh. 3 - Prob. 3.42ECh. 3 - Prob. 3.43ECh. 3 - The correlation between latitude and average...Ch. 3 - Prob. 3.45ECh. 3 - Prob. 3.46ECh. 3 - In a regression analysis, the total sum of squares...Ch. 3 - Prob. 3.48ECh. 3 - Suppose you know that the slope of a regression...Ch. 3 - Prob. 3.50ECh. 3 - Prob. 3.51ECh. 3 - Prob. 3.53ECh. 3 - Prob. 3.54ECh. 3 - Refer back to Exercise 3.7 about stopping distance...Ch. 3 - Prob. 3.56ECh. 3 - Prob. 3.57ECh. 3 - Prob. 3.58ECh. 3 - Prob. 3.59ECh. 3 - Prob. 3.60ECh. 3 - Prob. 3.61ECh. 3 - Prob. 3.62ECh. 3 - Prob. 3.63ECh. 3 - Prob. 3.64ECh. 3 - Prob. 3.65ECh. 3 - Prob. 3.66ECh. 3 - Prob. 3.67ECh. 3 - Prob. 3.68ECh. 3 - Prob. 3.69ECh. 3 - Prob. 3.70ECh. 3 - Prob. 3.71ECh. 3 - Given tickets for traffic violations than drivers...Ch. 3 - Prob. 3.73ECh. 3 - Prob. 3.74ECh. 3 - Prob. 3.75ECh. 3 - Prob. 3.76ECh. 3 - Prob. 3.77ECh. 3 - Prob. 3.78ECh. 3 - Prob. 3.79ECh. 3 - The heights (inches) and foot lengths (cm) of 33...Ch. 3 - Prob. 3.81ECh. 3 - The winning time in the Olympic men’s 500-meter...Ch. 3 - Prob. 3.83ECh. 3 - Prob. 3.84ECh. 3 - Prob. 3.86ECh. 3 - Prob. 3.87ECh. 3 - Prob. 3.88ECh. 3 - Prob. 3.89ECh. 3 - Use the dataset ceodata0t on the companion website...Ch. 3 - Prob. 3.91ECh. 3 - Prob. 3.92ECh. 3 - Prob. 3.93ECh. 3 - Prob. 3.94ECh. 3 - Prob. 3.95ECh. 3 - Prob. 3.96ECh. 3 - Prob. 3.97ECh. 3 - Prob. 3.98ECh. 3 - Prob. 3.99ECh. 3 - Prob. 3.100E
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- solve the question based on hw 1, 1.41arrow_forwardT1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an independent set and m(G) = |E(G)|. (i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The neighborhood of a vertex in a triangle free graph must be independent; all edges have at least one end in a vertex cover. (ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you may need to use either elementary calculus or the arithmetic-geometric mean inequality.arrow_forwardWe consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…arrow_forward
- Negate the following compound statement using De Morgans's laws.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forward
- Negate the following compound statement using De Morgans's laws.arrow_forwardCharacterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forward
- Prove sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forwardLet G be a connected graph that does not have P4 or C4 as an induced subgraph (i.e.,G is P4, C4 free). Prove that G has a vertex adjacent to all othersarrow_forwardWe consider a one-period market with the following properties: the current stock priceis S0 = 4. At time T = 1 year, the stock has either moved up to S1 = 8 (with probability0.7) or down towards S1 = 2 (with probability 0.3). We consider a call option on thisstock with maturity T = 1 and strike price K = 5. The interest rate on the money marketis 25% yearly.(a) Find the replicating portfolio (φ, ψ) corresponding to this call option.(b) Find the risk-neutral (no-arbitrage) price of this call option.(c) We now consider a put option with maturity T = 1 and strike price K = 3 onthe same market. Find the risk-neutral price of this put option. Reminder: A putoption gives you the right to sell the stock for the strike price K.1(d) An investor with initial capital X0 = 0 wants to invest on this market. He buysα shares of the stock (or sells them if α is negative) and buys β call options (orsells them is β is negative). He invests the cash balance on the money market (orborrows if the amount is…arrow_forward
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