ANL321_JUL_2022_TOA

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ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 1 of 6 ANL321 Timed Online Assignment - July Semester 2022 Statistical Methods Thursday, 17 November 2022 10:00 am - 12:00 pm Time allowed: 2 hours INSTRUCTIONS TO STUDENTS: 1. This Timed Online Assignment (TOA) contains 6 questions and comprises 6 pages (including cover page). 2. You must answer 6 questions. 3. If you have any queries about a question, or believe there is an error in the question, briefly explain your understanding and assumptions about that question before attempting it. 4. You MUST submit your answers via Canvas (similar to TMA submission) at the end time of this TOA (as stated on this cover page). The 15 minutes grace period as shown on Canvas is strictly meant for technical issues encountered during submission. Thereafter, you will not be able to submit your answers and you will be considered as having withdrawn from the course. No appeal will be allowed. 5. Your submission should consist of only one file and must not exceed 500MB in size. The file must be a Microsoft Word file saved in .docx format. All answers are to be typed. Flowcharts and graphs may be scanned or photographed and embedded in the Word file provided it does not exceed the file size limit of 500MB. Images of handwritten answers will not be marked . 6. To prevent plagiarism and collusion, your submission will be reviewed by Turnitin. The Turnitin report will only be made available to the marker and you will not be able to view it. 7. The University takes plagiarism and collusion seriously, and your Turnitin report will be examined thoroughly as part of the marking process.

ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 2 of 6 (Full marks: 100) Section A (50 marks) Answer all questions in this section. Refer to Question 1 for the background information to this section. Question 1 ------Start of Background Information ------ A cellphone manufacturer, NexTel, hired you as a consultant to study how satisfied its customers are in the four specific cellphone models they own. The company has been selling three of the models, Z1, Z2, and Z3, for a while now and recently introduced their new model, Z4, to the market. The total number of phones sold from January 2022 to March 2022 (i.e. first three months of 2022) is shown in Table 1 below. Table 1: Sales of phones by model (1st three months of 2022) Model Z1 Z2 Z3 Z4 Number of new phones sold from January 2022 to March 2022 130,000 90,000 77,000 3,000 Consider a simple random sample of 2000 phone owners from the above population with replacement. Each phone owner you sampled either owns a Z4 (i.e. the new model) or other models. ------ End of Background Information ------ Define the random variable X as “the number of Z4 owners” based on the random sample you obtained. Carefully explain what the distribution of X is and write down its distribution. (10 marks) Question 2 Explain, in your own words, what the expectation of a random variable is. Is the expectation of a random variable the same as the sample mean? Determine the expected number of Z4 owners and the standard deviation (i.e. the expectation and standard deviation of X). (15 marks) Question 3 From April to June 2022, NexTel ran a marketing campaign for the Z4 and in that quarter, the sales of the Z4 increased by 100%. NexTel’s Director of Marketing claimed that “this increase in sales reflects the success of the company’s marketing strategies for the Z4”. Write a report to the Chief

ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 3 of 6 Executive, not exceeding 1000 words, to appraise the Director’s statement. For instance, is the Director’s claim reasonable? Is the increase in sales necessarily reflects “success” of the marketing campaign? Are there situations that might undermine the Director’s claim? If so, how would you design a marketing campaign that will enable you to be confident that any "success" observed following the campaign is indeed due to the campaign itself? Feel free to provide your discussion to support your critique of the Director's statement. (25 marks)

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ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 4 of 6 Section B (15 marks) Answer all questions in this section. Refer to Question 4 for the background information to this section. Question 4 ------ Start of Background Information ------ You have been hired by a consulting firm, Vineyard Intelligence, as their head pollster. Your immediate responsibility is to predict the winner of the next presidential election. There are two candidates, Ann and Ben, vying for the president’s position. With your team, you polled a sample of potential voters randomly. ------ End of Background Information ------ Describe, carefully, the procedure you will implement to estimate the probability that Amy will win the election. Suppose you estimate that Amy's winning probability is 52 percent. Based on a 95% confidence interval, what minimum sample size will you need for your prediction to have a margin of error of 2 percent? (15 marks)

ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 5 of 6 Section C (35 marks) Answer all questions in this section. Refer to Question 5 for the background information to this section. Question 5 ------- Start of Background Information ------ Using a dataset on 880 houses sold in Stockton, CA in the mid 2000s, let us explore the relationship between house price ( PRICE ) and house size in square feet of living area ( SQFT ). The summary statistics for the variables (both in levels and in logs) are given in Table 2. Table 2: Summary Statistics - -------------------------------------------------------------------------------------- Variable | Obs Mean Std. Dev. Min Max Skewness Kurtosis ---------+---------------------------------------------------------------------------- price | 880 112810.8 52813.89 50000 500000 2.707592 14.77268 sqft | 880 1611.968 531.9902 704 4300 1.149429 4.940148 ln_price | 880 11.55446 .3764228 10.81978 13.12236 .8262437 4.03159 ln_sqft | 880 7.335504 .3115971 6.556778 8.36637 .2633583 2.747114 ------------------------------------------------------------------------------- ------- Note: price, sqft, ln_price and ln_sqft are names for the variable PRICE , SQFT , ln( PRICE ) and ln( SQFT ), respectively. Consider the log-linear model expressed by equation (1) below (1) The estimation output of the regression based on equation (1) is shown in Table 3. Table 3: Estimation output of equation (1) using ordinary least squares regression ------------------------------------------------------------------------------ Source | SS df MS Number of obs = 880 -------------+------------------------------ F( 1, 878) = 2143.38 Model | 88.3556977 1 88.3556977 Prob > F = 0.0000 Residual | 36.1934444 878 .041222602 R-squared = 0.7094 -------------+------------------------------ Adj R-squared = 0.7091 Total | 124.549142 879 .141694132 Root MSE = .20303 ------------------------------------------------------------------------------ ln_price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sqft | .000596 .0000129 46.30 0.000 .0005707 .0006212 _cons | 10.59379 .02185 484.84 0.000 10.5509 10.63667 ------------------------------------------------------------------------------ The summary statistics for the predicted (i.e. fitted) values of ln( PRICE ) and the residuals from the above regression are shown in Table 4. Table 4: Summary Statistics for the fitted values of ln( PRICE ) and the residuals ------------------------------------------------------------------------------- - ----- Variable | Obs Mean Std. Dev. Min Max Skewness Kurtosis ----------+--------------------------------------------------------------------------- fitted | 880 11.55446 .3170464 11.01335 13.15643 1.149429 4.940148 residuals | 880 -1.73e-10 .202918 -.710299 .9086631 .3239307 4.315611 ------------------------------------------------------------------------------- --------

ANL321 Copyright © 2022 Singapore University of Social Sciences (SUSS) TOA - July Semester 2022 Page 6 of 6 Note: fitted and residuals are the names for fitted values of ln( PRICE ) and the residuals, respectively. ------ End of Background Information ------ Referring to the regression results in Table 3, interpret the coefficient on SQFT . Explain if there is evidence to suggest that the size of the living area matters for home prices. If so, is the effect of size on home prices linear? (15 marks) Question 6 Before a bank issues a loan for a home purchase, it will first conduct a valuation on the house the buyer wants to put an offer on. The valuation is carried out by a team of in-house data scientists. You are hired by the Bank’s Chief of Data Science (CDS) to help the team create a statistical model to estimate the fair value of a house, which will be used for home valuation. Explain to the CDS whether equation (1) is a good model for estimating the fair value of home prices and why, and what are the potential issues to look out for. (20 marks) ----- END OF PAPER -----

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