Real Estate-CaseStudy
INTRODUCTION:
Statistics is a branch of mathematics, which involves:
1. Collecting data.
2. Organizing and analyzing data.
3. Drawing conclusions from data.
OBJECTIVE:
This case study is designed to develop students’ ability to assess and critically interpret statistics and business
information and apply them in changing business environments.
Assessment LearningOutcomes:
LO1-DiscreteandContinuous Probability Distributions(Chapters 5, 6, 7).
Analyze the probabilityof given business outcomesusingfundamentalprobabilityconceptsfordiscrete and continuousprobabilitydistributions.
LO2-Sampling Methods andCentral Limit Theorem(Chapter8).
Applyconcepts ofsamplingand the CentralLimitTheoremin obtaininginformation thatwillfacilitate the analysis ofappropriate businessissues.
LO3-EstimationandConfidenceIntervals(Chapter 9).
Computeprobabilityof given businessoutcomesbybuildingoneandtwo tailed confidenceintervals for
Zandtprobability distributions.
LO4, 5-One-Sample Tests ofHypothesis(Chapter10).
Testdifferentbusiness hypothesisbyapplyingtheconceptsof confidenceintervals, teststatistics, p-value, typeIandII errors, samplesizesandfinitepopulations.Drawstatistical inferences fromgiven business information,basedononeandtwo tailedhypothesis tests.
LO6: CorrelationandLinearRegression(Chapter13).
Assess thelikelyrelationships betweendependent andindependent variables inbusinesssituations using correlationandregressiontechniques.
Due Date:
Thehardandsoft copyof theproject
Theindividual presentationofthe project
MarkingAllocation:
Theprojectmarks areallocatedonagroupandindividual basis. Groupmarks areallocated basedoncorrectly answeringthequestions setintheprojectandhow,asagrouptheresultsandhowclearly thedataispresented.
Individuals willbegraded based upontheir contributiontothe presentation,explanationandunderstandingofthe data andhowtheyanswerquestions directed to themduringthepresentation.
Markingsplit:
•Group:80 %
•Individual:20%
GROUP Task1 Task2 Task3 Task4 Task5 Task6 Task7 TotalGroup
Grade Individual
Grade TotalGrade
Marks
Allocated 8 16 14 10 8 14 10 80 20 100
Marks
Obtained
Declaration:
No partofthis assignmenthasbeen copied fromanothersource, (notfromanothergroup orstudent, an internetsourceora book.
No partofthis assignmenthasbeen writtenforme by anyotherperson.
Name ID Signature
1.
2.
3.
4.
5.
OVERVIEW:
Referring to the Real Estate sales data, which reports information on 60homes sold in Al Reem Island area during the last year, there are many factors that can affect the selling price of homes such as the location, thenumber of bedrooms, number of bathrooms, the size of a home in a square feet, whether there is a pool or not, and whether there is a garage or not.
The main purpose of this study is to test if there is a relationship between Real estate sales prices and the above mentioned factors that seem to affect homes prices.
STEPS:
1) The data will be distributed to the students, each group will have a different data set as follows:
No. Price in
AED
Size of a home in square feet No. of Rooms No of bathrooms
Garage
Pool Distance Location
Keypoints to follow:
• Selling price in AED, the current price of the home evaluated by a professional.
• Size of the home in square feet: the total area of the house (including the garage, pool, etc.)
• Number of bedrooms: the no. of rooms in the house.
• No. of bathrooms: the no. of bathrooms in the house.
• Garage: 1 if the house has garage .zero if not. (1 = yes, 0 = no)
• Pool: 1 if the house has pool .zero if not. (1 = yes, 0 = no)
• Distance:the distance in Km between the HCT ADWC campus and the house.
• Location: the region in which the house is located
o 1: Abu Dhabi City
o 2: Khalifa city
o 3.Shahama
o 4.Bani Yas
o 5.Bahia
Refer to thedata givenby your teachercompletethefollowing tasks.
TASK1-Chapter5 (ASurveyof ProbabilityConcepts)
Construct a contingencytableasgiven below to answer the followingquestions: 2 marks
Location
1(AD) 2(Khalifa) 3(Shahama) 4(BaniYas) 5(Bahia)
Has Garage
Has No Garage
1. What approach of probabilitydidyou use? 1 mark
2. What is the probabilityof selecting a home with Garage? 1 mark
3. Find theprobabilityof selecting ahome in BaniYas? 1 mark
4. Calculate theprobabilityofselectinga home in Khalifaandhas Garage? 1 mark
5. What is the probabilityof selecting a home in Bahiaor has No Garage? 2marks
TASK2-A-Chapter6 (ProbabilityDistribution)
1. Use column “numberofbedrooms”tocreate aprobabilitydistribution. 2marks
2. Useyour probabilitydistribution to find theprobabilityof selectinga home with more than 3
Bedrooms. 1 mark
3. Usingthe probabilitydistribution table find the expected number ofbedrooms. 2marks
4. Find thevarianceusingtheprobabilitydistribution. 2marks
TASK2-B -Chapter6(Binomial Distribution)
5. Using MegaStatcreate abinomial distributionwith n=60, p=probabilityof selecting a home with a pooland explain what does the chart show? 2marks
6. Whatarethe expected number and the standard deviation of selecting a home with a pool? 2marks
7. What is the probabilitythatallhomeshave a pool? 1mark
8. What is the percentagethat fewer than15 homeshave a pool? 2marks
9. What is the probabilitythatbetween 23and 31 homeshave a pool? 2marks
TASK3: Chapter7(Continuous ProbabilityDistributions)
1. Computethe mean and thestandard deviation of thesales prices of the 60 homes. 2marks
2. What is the probabilitythat the area of the house would benomorethan2,000 square feet? 2marks
3. What is the probabilitythat the area of the house would beat least2,100 square feet? 2marks
4. What is the probabilitythat the area of the house would bebetween 2,200 square feetand 2,500 square feet? 2marks
5. About 68%of the areas of the houses fallbetween what two values?(UseEmpirical rule) 2marks
6. Between what twoareavalues does the middle 75% of homes (60 homes) fall? 2marks
7. What is the area of a house that separates thetop 20%from thelower 80%of the60homes? 2marks
TASK4: Chapter8 (SamplingMethods)
1. Select a sample A of16 homes from the60 homes dataset then paste it into anew sheet and name it as (SampleA).
Use systematicmethod and mention the system thatyou have used. 2 marks
2. Select a sample Bof 36homes from the60 homes dataset then paste it in a new sheet and name it as (SampleB). Use clustermethod and explain. 2 marks
3. Computethe mean, the standard deviation andthestandard errorofthehome prices of sample A. 2 marks
4. Compute themean, the standard deviation andthestandard errorofthehome prices of sample B. 1 mark
5. Compare answer 4)and5). Howcan the sampleerrorbereduced? 1 mark
6. What is the probabilitythat thehome prices ofsampleAwould beless than AED2,500,000? 2marks
TASK5:Chapter9 (Estimation and ConfidenceIntervals)
1. Computethe mean (µ) and the standard deviation (σ)of the home prices ofyour dataset
(60homes). 1mark
2. Forsample A,computethe meanand the standard deviation of home pricesforthe 16
homes
3. Forsample B, computethemeanand the standard deviation of thehome pricesforthe36 homes
4. ForSample A, what is thepointestimateof thepopulation mean of thehomes prices? 1mark
5. TheGovernment in Abu Dhabiwish to haveinformation on themean homes’ prices.Assumethat thepopulation standard deviation is AED 470,000.
ByusingSample A,what is a reasonablerangeofvalues forthe populationmean?(Use95%
confidencelevel). Use mean: ̅A and =470,000
Would it be reasonable to conclude that thepopulation homes’ prices mean is AED 2,000,000? 2marks
6. Assume that is unknown. ByusingSample B, construct a 90 percent confidenceintervalforthe population mean.[Use the mean and the standard deviation of Sample B]
Wouldit be reasonable to conclude that thepopulation homes’ prices mean is AED2,800,000? 2marks
7. Howlargeasample is needed to find thepopulations mean of thehomes prices within AED 150,000 at 99percentconfidence?Usethe standard deviation ofyourpopulation (60homes). 2marks
TASK6:Chapter10(One-SampleTestsof Hypothesis).
1. A researcher claims that theprices of homes in Abu Dhabi areless thanAED 2,500,000. Useyourdatasetof60 homes,and apopulation standard deviation of UAE is AED 470,000.
Is thereevidenceto support the claim at a0.05?Usethe traditional method. Show allthe steps. 6 marks
2. A researcher claims that thehome prices in Abu Dhabi are AED 3,000,000. ByusingSample
Band assuming that is unknown [Use the mean and the standard deviation ofSample B];
testthe claim at
a) 0.01 significance level
b) 0.05 significancelevel
Usethe P-value method.Show allthe steps. 8 marks
TASK7:Chapter13(Correlation andLinear Regression)
QUESTION TO ANSWER:Arethe home priceand the distance away from the city related?
1. Determinethe dependentvariable and theindependent variable. Describethe relationship
between the dependent variable and theindependent variable. Draw thescatter diagram ofyour dataset(60 homes). 2marks
2. Determinetheregression equation. What is a regression equation and whatis it used for? 2marks
3. What is the slope ofthe regression line? What does it represent? 1 mark
4. Statethe value ofY- intercept. Comment on its value. 1 mark
5. Statethe value of correlation coefficient. Comment on its value. 1 mark
6. Statethe value of coefficient ofdetermination.Comment on its value. 1 mark
7. Predict the selling price of a home 23 kilometers from the center of the city. Comment on the reliabilityofyour prediction.
1 mark
8. Estimatethe distance ofa home whoseprice is AED 2,900,000. Comment onyourestimation. 1 mark
GoodLuck
