Bundle: Understanding Basic Statistics, Loose-leaf Version, 8th + WebAssign Printed Access Card, Single-Term
8th Edition
ISBN: 9781337888981
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 5.2, Problem 4P
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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below.
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship.
Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size).
Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model.
Interpret the…
Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
Chapter 5 Solutions
Bundle: Understanding Basic Statistics, Loose-leaf Version, 8th + WebAssign Printed Access Card, Single-Term
Ch. 5.1 - Statistical Literacy List three methods of...Ch. 5.1 - Statistical Literacy Suppose a weather app says...Ch. 5.1 - Statistical Literacy What is the probability of...Ch. 5.1 - Statistical Literacy What is the law of large...Ch. 5.1 - Interpretation A Harris Poll indicated that of...Ch. 5.1 - Interpretation According to a recent Harris Poll...Ch. 5.1 - Basic Computation: Probability as Relative...Ch. 5.1 - Basic Computation: Probability of Equally Likely...Ch. 5.1 - Interpretation An investment opportunity boasts...Ch. 5.1 - Interpretation A sample space consists of 4 simple...
Ch. 5.1 - Critical Thinking Consider a family with three...Ch. 5.1 - Critical Thinking Consider the experiment of...Ch. 5.1 - Critical Thinking On a single toss of a fair coin,...Ch. 5.1 - Critical Thinking (a) Explain why -0.41 cannot be...Ch. 5.1 - Myers-Briggs: Personality Types Isabel Briggs...Ch. 5.1 - General: Roll a Die (a) If you roll a single fair...Ch. 5.1 - Psychology: Creativity When do creative people get...Ch. 5.1 - Agriculture: Cotton A botanist has developed a new...Ch. 5.1 - Expand Your Knowledge: Odds in Favor Sometimes...Ch. 5.1 - Expand Your Knowledge: Odds Against Betting odds...Ch. 5.1 - Business: Customers John runs a computer software...Ch. 5.2 - Statistical Literacy If two events are mutually...Ch. 5.2 - Statistical Literacy If two events A and B are...Ch. 5.2 - Basic Computation: Addition Rule Given P(A)=0.3...Ch. 5.2 - Basic Computation: Addition Rule Given P(A)=0.7...Ch. 5.2 - Basic Computation: Multiplication Rule Given...Ch. 5.2 - Basic Computation: Multiplication Rule Given...Ch. 5.2 - Basic Computation: Rules of Probability Given...Ch. 5.2 - Basic Computation: Rules of Probability Given...Ch. 5.2 - Critical Thinking Lisa is making up questions for...Ch. 5.2 - Critical Thinking Greg made up another question...Ch. 5.2 - Critical Thinking Suppose two events A and B are...Ch. 5.2 - Critical Thinking Suppose two events A and B are...Ch. 5.2 - Critical Thinking Consider the following events...Ch. 5.2 - Critical Thinking Consider the following events...Ch. 5.2 - General: Candy Colors MM plain candies come in...Ch. 5.2 - Environmental: Land Formations Arches National...Ch. 5.2 - General: Roll Two Dice You roll two fair dice, a...Ch. 5.2 - General: Roll Two Dice You roll two fair dice, a...Ch. 5.2 - General: Roll Two Dice You roll two fair dice, a...Ch. 5.2 - General: Roll Two Dice You roll two fair dice, a...Ch. 5.2 - General: Deck of Cards You draw two cards from a...Ch. 5.2 - General: Deck of Cards You draw two cards from a...Ch. 5.2 - General: Deck of Cards You draw two cards from a...Ch. 5.2 - General: Deck of Cards You draw two cards from a...Ch. 5.2 - Marketing: ToysUSA Today gave the information...Ch. 5.2 - Health Care: Flu Based on data from the...Ch. 5.2 - Focus Problem: Lie Detector Test In this problem,...Ch. 5.2 - Survey: Medical Tests Diagnostic tests of medical...Ch. 5.2 - Survey: Lung/Hear t In an article titled...Ch. 5.2 - Survey: Customer Loyalty Are customers more loyal...Ch. 5.2 - Survey: Sales Approach In a sales effectiveness...Ch. 5.3 - Statistical Literacy What is the main difference...Ch. 5.3 - Statistical Literacy Consider a series of events....Ch. 5.3 - Critical Thinking For each of the following...Ch. 5.3 - Critical Thinking You need to know the number of...Ch. 5.3 - TreeDiagram (a) Draw a tree diagram to display all...Ch. 5.3 - TreeDiagram (a) Draw a tree diagram to display all...Ch. 5.3 - Tree Diagram There are six balls in an urn. They...Ch. 5.3 - Prob. 8PCh. 5.3 - Multiplication Rule for Counting Four wires (red,...Ch. 5.3 - Multiplication Rule for Counting A sales...Ch. 5.3 - Counting: Agriculture Barbara is a research...Ch. 5.3 - Counting: Outcomes You toss a pair of dice. (a)...Ch. 5.3 - Compute P5,2.Ch. 5.3 - Compute P8,3.Ch. 5.3 - Compute P7,7.Ch. 5.3 - Compute P9,9.Ch. 5.3 - Compute C5,2.Ch. 5.3 - Compute C8,3.Ch. 5.3 - Compute C7,7.Ch. 5.3 - Compute C8,8.Ch. 5.3 - Counting: Hiring There are three nursing positions...Ch. 5.3 - Counting: Lottery In the Cash Now lottery game...Ch. 5.3 - Counting: Sports The University of Montana ski...Ch. 5.3 - Counting: Sales During the Computer Daze special...Ch. 5.3 - Counting: Hiring There are 15 qualified applicants...Ch. 5.3 - Counting: Grading One professor grades homework by...Ch. 5.3 - Counting: Hiring The qualified applicant pool for...Ch. 5.3 - Counting: Powerball The Viewpoint of this section,...Ch. 5 - Terminology Consider the following terms: sample...Ch. 5 - Terminology Consider the following situations:...Ch. 5 - Terminology Can two events that mutually exclusive...Ch. 5 - Terminology Consider two counting rules:...Ch. 5 - StatisticalLiteracy Consider the following two...Ch. 5 - Statistical Literacy If two events A and B are...Ch. 5 - Statistical Literacy If two events A and B are...Ch. 5 - Interpretation You are considering two facial...Ch. 5 - Interpretation You are applying for two jobs, and...Ch. 5 - Critical Thinking You are given the information...Ch. 5 - Critical Thinking You are given the information...Ch. 5 - Critical Thinking For a class activity, your group...Ch. 5 - Salary Raise: Women Does it pay to ask for a...Ch. 5 - Salary Raise: Men According to the same survey...Ch. 5 - General: Thumbtack Drop a thumbtack and observe...Ch. 5 - Survey: Reaction to Poison Ivy Allergic reactions...Ch. 5 - General: Two Dice In a game of craps, you roll two...Ch. 5 - Academic: Passing French Class records at Rockwood...Ch. 5 - Combination: City Council There is money to send...Ch. 5 - Basic Computation Compute....Ch. 5 - Counting: Exam Answers There are five...Ch. 5 - Scheduling: College Courses A student must satisfy...Ch. 5 - General: Combination Lock To open a combination...Ch. 5 - General: Combination Lock You have a combination...
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- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardProblem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forward
- Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forwardIn this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forward
- Using the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416plus+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200arrow_forward
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