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TSTA602 Assignment 2 May 11, 2020 Instructions. This assignment has a total of 30 marks and worth 30% of the final grade of TSTA602. The detailed marks allocation are provided at the beginning of each...

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TSTA602 Assignment 2 May 11, 2020 Instructions. This assignment has a total of 30 marks and worth 30% of the final grade of TSTA602. The detailed marks allocation are provided at the beginning of each question. You are encouraged to discuss the assignment with your peers, but must write down your own solution. This assignment is due at 5pm on Friday of Week 11 (12th June, XXXXXXXXXXPlease submit your assignment on Moodle before the deadline. 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. (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 XXXXXXXXXXd). (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 XXXXXXXXXXh). (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. 2
Answered Same Day May 26, 2021 TSTA602

Solution

Neenisha answered on Jun 06 2021
125 Votes
Part (a)
Scatter Plot of Price Vs Rent
Scatter Plot of Price Vs Cost
Part (b)
Model 1 Equation
Price = 259.7 + 0.08025 Rent
Model 2 Equation
Price = -6.302312 + 1.146005 Cost
Part (c)
Model 1 – level of significance
The p value of the x variable i.e. rent is 2e-16 which is less than 0.05, therefore reject null hypothesis at 5% level of significance and may conclude that rent is a significant variable impacting the apartment prices.
Model 2 - level of significance
The p value of the x variable i.e. cost is 2.2e-16 which is less than 0.05, therefore reject null hypothesis at 5% level of significance and may conclude that cost is a significant variable impacting the apartment prices.
Part (d) – Residual Plot
In the above graph, the residuals are randomly distributed implying that the relationship is linear. There are few outliers in the data, which are very far from other data points.
In the above graph, there is some patter which can be observed in the residuals, therefore there is a chance of heteroscedasticity in the data.
Part (e) – QQ Plot
The points in the above graph forms the straight line impliying that the variables come from normal distribution and data is not skewed.
    
The points in the above graph forms the straight line implying that the variables come from normal distribution and data is not skewed.
    
Part (f)
Model 3 - Equation
Price = 186.225 + 0.58148 Rent + 0.31591 Cost
Part (g) – Level of significance
The p value of the x1 variable i.e. rent is 8.11e-11 which is less than 0.05, therefore reject null hypothesis at 5% level of significance and may conclude that...
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