**Scenario**

You, as a property investor, are interested in understanding which factor (or factors) drives the prices of investment properties. A datasets 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 data set ’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: Model 3: apart price = d0 + d1rent + d2cost Write down the equation of the model with correct coefficients. 1

(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 1 and Model 3.

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