Quantitative Methods For Finance & Accounting Assignment 1
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.
Bank X provides home loan service to their retail customers and charge a interest rate for their service. Due to market fluctuations, Bank X only offers floating interest rate (FIR) for their home loan customers.
A friend of you who works as a banker at Bank X told you that the average yearly FIR in the last thirty years follows a Normal distribution with mean 3.2% (i.e., µ = 0.032) and standard deviation 0.04 (i.e., σ = 0.04). In addition, a sample of size 10 (drawn from N(0.032, 0.0016)) is available to you which has been summaried in the table below -0.021 0.029 -0.009 -0.002 0.002 -0.006 0.006 -0.064 0.023 0.031
Table 1: A sample of FIR Your friend seek help from you to use your knowledge from TSTA602 to assist Bank X to do the following data analysis. Please write a report to answer all the following questions.
(a). (3 marks) calculate (mannually) the sample mean, and sample standard deviation for the sample in Table 1.
(b). (4 marks) if we draw samples of sizes 10 many times and form a distribution of sample mean, state the distribution of the sample mean and provide the reason for your conclusion; calculate the mean of the sample means and its standard deviation.
(c). (5 marks) based on (b), find the probability that the sample mean is smaller than 0.02. Please keep two decimal places in the calculation of standardization.
(d). (2 marks) if the sample mean from (a) is your observed value, calculate the 95% confidence interval for the sample mean.
(e). (2 marks) An outlier is a data point outside the interval [Q1 − 1.5IQR, Q3 + 1.5IQR], where Q1 and Q3 are first and third quartile respectively, and IQR 1 is the interquartile range. Explain whether there is any outlier appears in the sample in Table 1? You can calculate Q1 and Q3, and IQR using R (in Rstudio).
(f). (4 marks) Use R (in Rstudio) to generate 1,000,000 samples of size 10 from N(0.032, 0.0016) (please set the seed equals to 602), compute the sample mean for each of these samples, draw a boxplot (set the frequency parameter to FALSE) for these sample means and add a density curve to the boxplot. Please provide the histgram with the density curve here and attach your R code as appendix
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