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.

(a). (2 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). (4 marks) Comment 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:

Model3: apart price=d0+d1rent+d2cost Write down the equation of the model with correct coefficients.

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(g). (3 marks) Comment 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 = 810 and cost = 800, predict the prices under Model

apart_price    rent     cost_of_property

540     350     475

550     360     485

555     370     490

560     380     495

570     385     505

575     395     510

580     400     515

590     415     520

600     420     530

605     430     535

610     440     540

620     450     550

625     455     555

635     465     560

640     480     565

650     485     570

660     490     580

665     505     585

670     510     590

680     520     600

685     530     605

690     540     610

700     545     615

710     560     620

715     565     625

720     575     630

730     580     640

735     595     645

740     600     650

750     610     660

755     620     665

765     630     670

770     640     675

780     645     680

785     655     690

790     665     695

800     675     705

810     680     710

815     690     715

825     705     720

830     710     725

835     720     730

845     725     740

850     735     755

860     750     760

865     755     765

870     760     770

880     775     775

885     780     780

900     800     795