ECO220_TT1

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Feb 20, 2024

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ECO220Y1Y – LEC5101, Term Test #1, Instructor: Xiner Xu May 30, 2022, 6:10 – 8:00 pm U of T E-MAIL: ___________________________________@MAIL.UTORONTO.CA SURNAME (LAST NAME): GIVEN NAME (FIRST NAME): UTORID: (e.g. LIHAO118) Duration: 1 hour and 50 minutes Aids Allowed: A non-programmable, non-graphing calculator Instructions: • Keep these test papers and the Supplement closed and face up on your desk until the start of the test is announced. You must stay for a minimum of 60 minutes. • There are 4 questions (most with multiple parts) with varying point values worth a total of 100 points. • This test includes these 8 pages plus the Supplement . The Supplement contains the aid sheets, readings, figures, tables, and other materials for some test questions. For each question referencing the Supplement , carefully review all materials. The Supplement will NOT be collected: write your answers on these test papers. When we announce the end of the test, hand these test papers to us (you keep the Supplement ). • Write your answers clearly, completely, and concisely in the designated space provided immediately after each question. An answer guide ends each question to let you know what is expected. For example, a quantitative analysis (which shows your work and reasoning), a fully labelled graph, and/or sentences. o Anything requested by the question and/or the answer guide is required. Similarly, limit yourself to the answer guide. For example, if the answer guide does not request sentences, provide only what is requested (e.g. quantitative analysis). o Marking TAs are instructed to accept all reasonable rounding. • Your entire answer must fit in the designated space provided immediately after each question. No extra space/pages are possible. You cannot use blank space for other questions, nor can you write answers on the Supplement . Write in PENCIL and use an ERASER as needed so that you can fit your final answer (including work and reasoning) in the appropriate space. Questions give more blank space than is needed for an answer (with typical handwriting) worth full marks. Follow the answer guides and avoid excessively long answers.

(1) [21 pts] See Supplement for Question (1): Performance Review at a Paper Company (a) [4 pts] Circle the correct answers. i. This is an example of cross-sectional/time series/panel data. ii. Number of sales is a/an categorical/Bernoulli/dummy/interval variable. (b) [4 pts] What is the average number of sales a salesperson made in April? Answer with a quantitative analysis. (c) [4 pts] What is the IQR? Answer with a quantitative analysis that makes your reasoning clear. Is the IQR you found a parameter or a statistic?

(d) [6 pts] What is the standard deviation of the number of sales a salesperson made in April? (e) [3 pts] If we standardize number of sales, what will be the smallest value of the standardized variable? Answer with a quantitative analysis that makes your reasoning clear.

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(2) [28 pts] See Supplement for Question (2): The Canadian Labour Force Survey (a) [8 pts] For a frequency histogram with the same bin width, what would be the height of the tallest bar? Answer with a quantitative analysis that makes your reasoning clear. (b) [6 pts] TRUE/FALSE/UNCERTAIN: To make the histogram more symmetric, we can standardize the usual hourly wages variable. After standardization, half of the observations will be positive, and the other half will be negative. Answer and explain in 3-4 sentences.

(c) [6 pts] Is the median log(hourly wage) the same as the log(median hourly wage) ? Answer and explain in 1-2 sentences. Is the mean log(hourly wage) the same as the log(mean hourly wage) ? Answer and explain in 1-2 sentences. (d) [2 pts] A Member of Parliament introduced an economic reform bill. The bill offers all workers an additional $2 per hour, and increases their hourly income by 10% (including the $2). Write down the equation that describes the transformation from the initial hourly income ( 𝑤 0 ) to the new total take-home hourly income ( 𝑤 1 ). (e) [6 pts] Write down the two equations that describe the transformation from the initial sample mean ( 𝑤 ̅ 0 ) to the new sample mean ( 𝑤 ̅ 1 ), and from the initial sample variance ( 𝑠 0 2 ) to the new sample variance ( 𝑠 1 2 ). How does the proposed bill affect income equality?

(3) [12 pts] See Supplement for Question (3) . Create the correlation matrix. Keep at least 2 decimal places to avoid rounding errors. You will not receive credit if you fail to show the work. (4) [39 pts] See Supplement for Question (4): Class Attendance and Academic Performance (a) [4 pts] What is the 𝑅 2 of Regression 1? Answer with a quantitative analysis. What is the interpretation of 𝑅 2 in the context of this regression? Answer with 1 precise sentence.

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(b) [16 pts] Consider the following alternatives to Regression 1. Compare each of them with Regression 1 and fill in the blanks with “larger”, “smaller”, or “the same”. i. If we regress “ final ” on “ atndrte ” , 𝑠 𝑒 will be , and 𝑅 2 will be . ii. If regress the adjusted final on “ attend ” , where the adjusted final is the final exam score out of 100 instead of 40, SSE will be , the slope will be , and 𝑅 2 will be . iii. If we randomly delete half of the observations, we should expect that the variance of the dependent variable will be , SST will be , and 𝑅 2 will be . (c) [4 pts] What does the number -0.08106 in Regression 2 mean? Answer with 1 precise sentence that interprets it. (d) [3 pts] What does the number 2.96455 in Regression 3 mean? Answer with 1 precise sentence that interprets it.

(e) [4 pts] What kind of graph is Figure 1? What important information about the residuals does it tell us? Answer and explain with 2-3 sentences. (f) [3 pts] If we regress “ priGPA ” on “ never_missed ” , what will the estimated OLS line be? Answer with 1 equation. (g) [5 pts] Is “ attend ” an endogenous or exogenous variable in Regression 1? How does Regression 3 help you answer this question? Answer with 2-3 sentences.

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