NCC 5010 - 2023 Practice Final 1 Solution

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Cornell University *

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5010

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Jan 9, 2024

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1 NCC 5010: Data Analytics and Modeling Practice Final 1 Read Carefully: 1. Write your student ID and net ID below. Do not put your name on this exam. 2. You may have two 8 ½ by 11 sheet of paper with notes on both sides. Other than that, the exam is closed book and closed notes. Laptops and communication devices are not allowed. You are not allowed to share any materials or equipment. 3. You have 3.0 hours to complete this exam. The exam has 6 problems . Points for each problem are indicated. Some problems will take longer than others, so plan your time accordingly. 4. Write your solutions in the space provided in this document using the front and back of sheets as necessary. 5. Show all of your calculations clearly. $QVZHUV OLNH ³WUXH´ RU MXVW D VLQJOH QXP ber are not satisfactory and will not be given partial credit. If we cannot locate where your solution is written, you will not receive credit. State your assumptions if you must make any assumptions not given in a question. 6. Taking this exam indicates that you understand and will abide by the Cornell University Code of Academic Integrity. 7. Some common z-statistics: 3±] ²µ¶·¸¹ ºµºº¶ 3±] ²µ»²¸¹ ºµº¼ 3±] ¼µ½¸º¹ ºµº²¶ 3±] ¼µ¸¾¶¹ ºµº¶ ________________________________________________________________________ Student ID# ______________________________ Net ID# ______________________________ Do not write below this line. ________________________________________________________________________ Q1: Q2: Q3: Q4: Q5: Q6: Total: /25 /16 /18 /15 /13 /14
2 Question 1: (25 points) You are an executive at a large book publisher, Bean Publishing. Bean Publishing uses a regression model to examine several factors that influence how much a customer spends on leisure books every year. The regression output is below. The dependent variable is book sales per customer (in $). The independent variables are: x Income (in $) ± t KH FXVWRPHU¶V PRQWKO\ LQFRPH x College (0 or 1) ± D GXPP\ YDULDEOH WKDW LV VHW WR ³¼´ LI WKH FXVWRPHU KDV D FROOHJH HGXFDWLRQ x DigitalReader (0 or 1) ± D GXPP\ YDULDEOH WKDW LV VHW WR ³¼´ LI WKH FXVWRPHU RZQV D n e-reader x IncomeXDigitalReader (in $) ± Income multiplied by DigitalReader x Age (in years) ± WKH FXVWRPHU¶V DJH x AgeSQ (in years squared) ± Age squared x Children ± A categorical variable with one of three possible options (there is no missing data): 1. AdultChildren (0 or 1) ± a dummy variable that is set WR ³¼´ LI WKH FXVWRPHU KDV DGXOW FKLOGUHQ 2. NoChildren (0 or 1) ± D GXPP\ YDULDEOH WKDW LV VHW WR ³¼´ LI WKH FXVWRPHU KDV QR FKLOGUHQ 3. Children (0 or 1) ± D GXPP\ YDULDEOH WKDW LV VHW WR ³¼´ LI WKH FXVWRPHU KDV QRQ -adult children Use this information to answer the following questions. a. Why is the value for R-squared so close to the value for adjusted R-squared? Regression Statistics Multiple R 0.409 R Square 0.167 Adjusted R Square 0.167 Standard Error 33.788 Observations 20000 ANOVA df SS MS F Significance F Regression 8 4,591,233 573,904 503 0 Residual 19,991 22,822,847 1,142 Total 19,999 27,414,080 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 85.536 0.716 119.518 0.000 84.133 86.939 Income 0.003 0.001 2.934 0.003 0.001 0.004 College 2.129 0.782 2.724 0.006 0.597 3.661 DigitalReader -7.280 2.205 -3.302 0.001 -11.601 -2.959 IncomeXDigitalReader 0.012 0.005 2.215 0.027 0.001 0.022 Age 0.867 0.092 9.433 0.000 0.687 1.047 AgeSQ -0.016 0.003 -5.662 0.000 -0.022 -0.011 AdultChildren 0.113 0.828 0.136 0.892 -1.511 1.736 NoChildren -31.786 0.556 -57.155 0.000 -32.876 -30.696 3 The number of independent variables is small relative to the sample size , so the penalty factor (nn) for adjusted R2 is small .
3 b. Estimate the average amount spent on leisure books for a 35 year old customer with an annual income of $60,000, no college education, no children, and who owns an e-reader. c. Provide an economic interpretation of the impact of NoChildren on the amount spent on leisure books. d. Provide an economic interpretation of the coefficient on the Intercept. e. Provide an economic interpretation of the impact of College on the amount spent on leisure books. f. If a customer has an e-reader, what is the impact of a $1,000 LQFUHDVH LQ WKH FXVWRPHU¶ s monthly income on the amount spent on leisure books? g. If a customer is 50 years old, what is the impact RI D ¼ \HDU LQFUHDVH LQ WKH FXVWRPHU¶V DJH on the amount spent on leisure books? 3 3 4 3 4 5 $ / Mo . % ' lo $ / no ⑨ = 85.536 + a 003 ( Income )+ 2.129 ( College ) - 7.280 ( BR ) -1.012 ( the ✗ DR ) yrs yrs sq + . 867 Age - . 016 Ages Q + . 113 Adult -31.786 ( No child ) = 85.536 + . 003 ( b + 2- 129 ( o ) - 7.280 (1) + . 012 ( ¥ 0 ✗ 1) + . 867 ( 35 ) - . 016 ( 352 ) + < 113 ( o ) - 31.786 (1) = $ 132.22 Relative to a customer that has non - adult children , a customer with no children spends $ 31.786 less on books every year . A customer that has a zero valve for every variable is expected to spend $ 85.53b on books every Year . Relative to a customer without a college education a customer with a college education is expected to pay $ 2.129 more on books every year . tdy = • 003 ( ☐ Inc ) + . 012 ( A- Inc ✗ DR ) = . 003 ( 1000 ) + . 012 ( 1000 ✗ 1) = $ 15 Js , = stuff . - + . 867 ( 51 ) - . 016 ( 517 + stuff js-o-f.fi/-.t.867(5o)-.016(5o)2-stvft-#Ay = - $ 0.75
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