TSTA602 Assignment 2 September 7, 2021 Instructions. Assignment 2 has a total of 40 marks and worths 40% of the final grade of TSTA602. The detailed mark allocations are provided at the beginning of each question. Unless otherwise specified, please calculate your answer to two decimal places if approximation is needed. This assignment is due at 5pm on Friday, 1st October 2021 (Week 9). 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 assignment, 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 onebedroom 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. Comment on the significance of all coefficients obtained from (b) based on the pvalues (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. 1 (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. Comment on the significance of all coefficients obtained from (f) based on the pvalues (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.

apart_price	rent	cost_of_property
500	177	55
505	182	60
515	197	65
520	209	70
525	213	72
535	219	75
540	226	72
550	233	71
555	242	70
570	258	68
585	271	63
590	279	60
595	296	71
600	301	73
615	307	78
620	314	80
625	326	82
630	334	85
635	341	81
645	343	80
660	355	91
665	373	93
670	379	95
675	383	97
685	387	96
695	408	95
710	419	93
720	423	92
725	431	91
730	437	94
735	446	97
750	457	99
755	463	100
765	472	104
770	482	103
775	497	101
785	502	101
795	508	97
800	518	90
805	527	95
810	534	101
815	541	103
825	553	104
835	562	96
840	565	98
845	573	91
860	586	87
875	597	110
890	611	112
905	628	115