apart_price,rent,cost_of_property 500,350,300 505,360,305 515,370,310 520,380,320 525,385,330 535,395,340 540,400,350 550,415,360 555,420,370 570,430,380 585,440,390 590,450,400 595,455,410 600,465,365 615,480,370 620,485,375 625,490,380 630,505,385 635,510,390 645,520,395 660,530,400 665,540,405 670,545,410 675,560,415 685,565,420 695,575,425 710,580,430 720,595,435 725,600,440 730,610,445 735,620,450 750,630,455 755,640,460 765,645,465 770,655,470 775,665,475 785,675,480 795,680,485 800,690,490 805,705,495 810,710,500 815,720,505 825,725,510 835,735,515 840,750,520 845,755,525 860,760,530 875,775,535 890,780,540 905,800,545
TSTA602 Assignment 2
September 28, 2020
Instructions. Assignment 2 has a total of 40 marks and worths 40% of the final grade of TSTA602. The detailed marks allocation are provided at the beginning of each question. Unless otherwise specified, please calculate your answer to two deci- mal places if approximation is needed. This assignment is due at 5pm on Friday of Week 10 (23rd October, 2020). Please submit your assignment before the deadline, no late submission will be accepted unless a pre-approval from Lecturer is obtained. The assignment must be submittded via Moodle in a pdf format with the file name ’firstname surname studentID.pdf’. Any assignment submitted through email (without pre-approval) will not be marked. Although this is an individual as- signment, you are encouraged to discuss the assignment with your peers, but must write down your own solution. Penalties will apply if two solutions have a high similarity.
Scenario. You, as a property investor, are interested in understanding which factor (or factors) drives the prices of investment properties. A dataset is collected which contains the prices (in thousand dollars, as denoted by apart price) for 50 one- bedroom apartments in city X, their corresponding rents per week (in dollars, as denoted by rent) and the costs to hold each of these properties per week (in dollars, as denoted by cost of property). Following the procedures below to analyse the dataset ’assign2 data.csv’ by using Rstudio. Please only include relevant outputs from Rstudio in your solution and attach the R codes as appendice (2 marks for attach R codes).
(a). (3 marks) Import the data into Rstudio, draw two scatter plots: apart price versus rent and apart price versus cost.
(b). (4 marks) Fit the following two linear models:
Model 1: apart price = b0 + b1 × rent
Model 2: apart price = c0 + c1 × cost
Write down the equations of the two models with correct coefficients.
(c). (8 marks) Written down the p-values from the output of your R codes. Com- ment on the significance of all coefficients obtained from (b) based on the p- values (from the outputs of Rtudio). The significance level is 0.05.
(d). (6 marks) Produce residual plots for each model in (b), comment on each plot.
(e). (4 marks) Produce normal qq plots for each model in (b), and comment on each plot.
(f). (3 marks) Fit the following linear model:
Model 3: apart price = d0 + d1rent + d2cost
Write down the equation of the model with correct coefficients.
(g). (6 marks) Written down the p-values from the output of your R codes. Com- ment on the significance of all coefficients obtained from (f) based on the p- values (from the outputs of Rtudio). The significance level is 0.05.
(h). (2 marks) Compare Model 1 and Model 3, explain which one is better.
(i). (2 marks) Given rent = 900 and cost = 650, predict prices under Model 1 and Model 3.