Learning outcome: - Apply matrix algebra to summarize and process multivariate data. - Construct linear and logistic reg
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Learning outcome: - Apply matrix algebra to summarize and process multivariate data. - Construct linear and logistic regression models to solve business prediction problems. Instructions: (Marks would be deducted if you fail to follow the instructions below.) - In answering the questions of the assignment, show clearly the steps you take in arriving at your solutions for each question. Keep at least four decimal places in the final answer for statistical computations or otherwise specified. - Except Question 5 which require you to utilize R, the rest of the questions must be answered manually. - The soft copy of handwritten or typed answers of Questions 1 to 4 and the analysis report for Question 5 (in Word) must be uploaded to OLE by the due date. The R program of Question 5 must also be uploaded to "Assignment 1−R program". - This is an individual assignment. Copying some or all of another student's assignment or R program is plagiarism. (Note: The assignment will be checked by Turnitin and zero mark will be given to plagiarized works.) Question 1 (8 marks) Let A=[644−1],B=[42−25],C=[2−3−1]′ and D=⎣⎡1−23⎦⎤ Perform the following operations. (a) A−B and A′+B (2 marks) (b) CD′ (2 marks) (c) BA′ (2 marks) (d) ∣∣A−1∣∣∣∣B−1∣∣ (2 marks) Question 2 (10 marks) Solve the following system of equations by Matrix method: X1+2X2−3X3=52X1+X2−4X3=7X1+X2+X3=10 (Note: zero mark will be given for non-matrix method.) Question 3 (10 marks) Let E=[−2635]. Determine the eigenvalues and normalized eigenvectors of E.
Question 4 (12 marks) Let Σ=⎣⎡161−1136−2−1−24⎦⎤ be the covariance matrix of the random vector X=⎣⎡X1X2X3⎦⎤. (a) Determine V1/2,(V1/2)−1 and ρ. (6 marks) (b) Find the covariance matrix for the linear combination 2X1−X2+X3. (3 marks) (c) Find the covariance matrix for the following linear combinations of X1,X2 and X3. Z1=X1+X2+2X3Z2=X1−2X2+X3 (3 marks) Question 5 (60 marks) A researcher wishes to predict the selling price of apartments of a Taiwan City using multiple linear regression model. A random sample of 414 flats that is sold were randomly selected to form a dataset "real_estate_valuation.csv". The dataset includes the following six variables: The dependent variable is "house_price". The "real_estate_valuation.csv" dataset can be downloaded from the OLE.) (a) Utilize R to determine the multiple linear regression model to predict the house_price by considering which independent variable(s) be included in the model among the other given variables using stepwise regression (forward). You are expected to perform relevant model checking including relevant graphs plotting after the desired model is formulated. All R programs must be included in the answer and marks will be deducted if failing to do so. (40 marks) (b) Perform relevant hypothesis testing to assess the validity of the multiple linear regression model obtained as well as the validity of individual regression coefficients. (5 marks) (c) Interpret the regression coefficients of the model. (5 marks)
Question 5 (60 marks) A researcher wishes to predict the selling price of apartments of a Taiwan City using multiple linear regression model. A random sample of 414 flats that is sold were randomly selected to form a dataset "real_estate_valuation.csv". The dataset includes the following six variables: The dependent variable is "house_price". The "real_estate_valuation.csv" dataset can be downloaded from the OLE.) (a) Utilize R to determine the multiple linear regression model to predict the house_price by considering which independent variable(s) be included in the model among the other given variables using stepwise regression (forward). You are expected to perform relevant model checking including relevant graphs plotting after the desired model is formulated. All R programs must be included in the answer and marks will be deducted if failing to do so. (40 marks) (b) Perform relevant hypothesis testing to assess the validity of the multiple linear regression model obtained as well as the validity of individual regression coefficients. (5 marks) (c) Interpret the regression coefficients of the model. (5 marks) (d) Write a reflective journal of not more than 200 words that summarizes your learning experience in applying knowledge and skills acquired in the course to build the regression model for the given problem, and that explain how this experience could enrich your ability to apply course knowledge to real life applications. (10 marks)