The lab had you specify and fit both models. This homework is the other half of the skill: reading model output that someone else fit, the way you will read a model a colleague or an AI hands you. Twenty multiple-choice questions, each one a piece of fitted output and one correct reading of it.
This page is the readable version of Homework 8 - the questions to study and explore with the AI. The graded submission happens in the Canvas New Quiz: 20 questions, 5 points each, 100 points total. There are no radio buttons here and no answers are shown.
Start here
Choosing the right answer means you understood the concept, not that you memorized a formula. Everything is grounded in one dataset, the same Summit Gear file from Lab 8 - 2,200 B2B customer accounts. The continuous target is days_to_pay (average days an account takes to pay an invoice). The binary target is defaulted (1 = a receivable went bad and was written off; base rate about 20%). The numbers you read are illustrative in-sample fits on this one dataset - read them for the lesson they teach, not as a claim about how good the model is.
What you'll need
The Excel workbook with the regression already built - summit_gear_customers.xlsx. Your instructor supplies a version with the OLS regression already run, so you open it and read the output directly. It has two tabs: a Read me tab that explains the columns, and a Data tab with all 2,200 accounts. Part of this homework is opening that file and examining the regression output it shows you.
Twenty multiple-choice questions, 5 points each, 100 points total. Answer in the Canvas New Quiz. No file upload, no notebook to submit, no written essays. No time limit; resubmit as many times as you like, latest attempt kept. A worked answer key is released after the deadline.
Using AI on this homework
This is an AI-first course. You are encouraged to use the AI tutor on this page - and, for the logistic section, the linked Python notebook - to explore the data and check your understanding before you answer. Open the workbook, ask the AI to walk you through a coefficient or an odds ratio, load the CSV and re-fit a model to see what moves. The AI writes the Python; your job is to specify what to look at, validate the output, and interpret what it means. Because every question is multiple choice, the work that counts is understanding why the right option is right.
Section A - Read the OLS regression output
Questions 1-5
Open the Excel workbook your instructor supplied and find the regression output already built on it. Summit Gear fit an OLS regression of days_to_pay on every numeric predictor in the file (the full "kitchen sink" model). The table below is that output - the same figures you see in the workbook - so you can read your answers off either one:
R² = 0.844, adjusted R² = 0.843, n = 2,200.
OLS regression of days_to_pay on every numeric predictor
term
coefficient
std err
t
P-value
const (intercept)
23.43
0.930
25.19
0.000
credit_limit
-0.00000
0.00003
-0.11
0.915
avg_balance
0.00078
0.00009
9.02
0.000
annual_spend
0.00001
0.00001
1.76
0.079
prior_late_count
3.339
0.111
30.04
0.000
days_since_last_order
0.026
0.006
4.28
0.000
orders_per_year
-0.192
0.033
-5.91
0.000
discount_rate
-1.696
0.077
-22.06
0.000
avg_order_value
0.00004
0.00004
1.03
0.303
noise_a
0.003
0.010
0.30
0.767
noise_b
0.004
0.005
0.76
0.448
Question 1
The prior_late_count coefficient is +3.339. Holding the other predictors fixed, this means:
AEach additional prior late payment is associated with about 3.3 fewer days to pay.
BCustomers with prior late payments take 3.339 days to pay, on average.
CEach additional prior late payment is associated with about 3.3 more days to pay.
DAbout 3.3% of the variation in days_to_pay is explained by prior late payments.
Question 2
The discount_rate coefficient is -1.696. A customer's average discount rises from 2 percentage points to 5 percentage points (a 3-point increase). The model expects their predicted days_to_pay to:
Aincrease by about 5 days.
Bdecrease by about 5 days.
Cdecrease by about 1.7 days.
Dstay the same, because discount alone cannot change payment timing.
Question 3
The R² for this model is 0.844. The best plain-language reading for a non-analyst on the collections team is:
AThe model explains about 84% of the variation in how long customers take to pay; the rest is other factors or random variation.
BThe model predicts each customer's payment date correctly 84% of the time.
CThe model is 84% accurate.
D84% of customers pay their invoices on time.
Question 4
orders_per_year has coefficient -0.192 and a P-value of 0.000, so it is statistically significant. A teammate says, "Significant means important, so order frequency is a big driver of payment timing." The best response is:
ACorrect - a statistically significant predictor is always a large driver.
BWrong - a significant predictor should always be dropped from the model.
CCorrect - the negative sign proves it is the single biggest driver.
DWrong - significance means the effect is reliably non-zero, but the small coefficient (-0.192) means even 10 more orders a year move predicted payment timing by under 2 days, so the effect is real but small.
Question 5
days_since_last_order has coefficient +0.026 and is statistically significant. Which reading is correct?
AAn account that last ordered 100 days ago is predicted to take about 26 days longer to pay.
BAn account that last ordered 100 days ago is predicted to take about 2.6 days longer to pay than one that ordered today, holding the other predictors fixed.
Cdays_since_last_order has no effect, because the coefficient is small.
DEach additional day since the last order adds about 2.6 days to predicted payment time.
Section B - Spot multicollinearity from a correlation matrix
Questions 6-9
When two predictors move together closely, the model cannot tell their separate effects apart, and their individual coefficients become unstable and hard to trust. The simplest way to spot the risk is a correlation matrix: a hot off-diagonal cell - a pair correlated close to 1.0 (or close to -1.0) - is the warning sign. Here is the correlation matrix for five of the predictors above:
Correlation matrix for five predictors
credit_limit
avg_balance
annual_spend
prior_late_count
discount_rate
credit_limit
1.00
0.98
0.96
0.04
-0.01
avg_balance
0.98
1.00
0.99
0.05
0.00
annual_spend
0.96
0.99
1.00
0.03
0.02
prior_late_count
0.04
0.05
0.03
1.00
0.02
discount_rate
-0.01
0.00
0.02
0.02
1.00
Question 6
Reading the matrix, which pair of predictors shows the clearest sign of a multicollinearity risk?
Aprior_late_count and discount_rate (correlation 0.02).
Bavg_balance and discount_rate (correlation 0.00).
Ccredit_limit and avg_balance (correlation 0.98).
Dcredit_limit and prior_late_count (correlation 0.04).
Question 7
credit_limit, avg_balance, and annual_spend all correlate 0.96 to 0.99 with one another. What real thing about a customer explains why these three columns move together so tightly?
AThey are all proxies for the same underlying thing - the customer's account size, how big a customer they are - expressed in different units.
BThey are all measures of how late the customer pays.
CThey are random noise columns with no meaning.
DThey are all categorical region codes.
Question 8
Outside this dataset, which pair of variables is most likely to cause a multicollinearity problem, because the two columns carry essentially the same information?
AA customer's region and their days_since_last_order.
BA customer's customer_id and their discount_rate.
CA customer's segment and their prior_late_count.
Dannual_revenue measured in dollars and annual_revenue measured in thousands of dollars.
Question 9
The analyst keeps avg_balance and drops credit_limit and annual_spend. In the re-fit model, avg_balance's coefficient settles at +0.00090 and is stable. What is the consequence of leaving all three in, and why is keeping just one enough?
ALeaving all three in makes the model run out of memory; the fix is to add more rows.
BLeaving all three in makes their individual coefficients unstable and hard to trust; one column is enough because the three carry nearly the same information, so one representative captures the signal without the instability.
CLeaving all three in drops R² to zero; the fix is to remove prior_late_count.
DNothing happens - including three near-identical columns never affects a regression.
Section C - Read the logistic output
Questions 10-13
Summit Gear fit a logistic regression of defaulted on four payment-behavior predictors. The default base rate is 19.9%. Your instructor also supplies a short Python notebook (link on the Week 8 page) so you can load the data, re-fit the model, and read off a predicted probability for any customer you build. The fitted output:
Logistic regression of defaulted on four predictors
term
coefficient
odds ratio (exp of coef)
P-value
const (intercept)
-3.261
—
0.000
prior_late_count
0.624
1.867
0.000
discount_rate
0.213
1.238
0.000
days_since_last_order
0.0041
1.0041
0.072
orders_per_year
-0.021
0.979
0.107
Two example customers, scored by this model:
Customer A (no prior lates, low discount, recent order, frequent orders): predicted probability of default ≈ 0.02.
Customer B (six prior lates, high discount, long since last order, infrequent orders): predicted probability of default ≈ 0.95.
Question 10
The prior_late_count odds ratio is 1.867. Holding the other predictors fixed, each additional prior late payment:
Amultiplies the customer's odds of default by about 1.87 - roughly an 87% increase in the odds.
Bmultiplies the customer's probability of default by about 1.87.
Cincreases the probability of default by exactly 87 percentage points.
Dhas no effect, because 1.867 is close to 1.
Question 11
A customer has 3 more prior late payments than an otherwise identical customer. The odds ratio is multiplicative. By what factor are that customer's odds of default higher?
Aabout 5.6× (1.867 × 3).
Babout 1.87×.
Cabout 6.5× (1.867³).
Dabout 3×.
Question 12
Customer B's predicted probability of default is 0.95. Converting that probability to odds (p ÷ (1 − p)):
Aabout 1 to 19 against default.
Babout 0.95 to 1.
Cabout 2 to 1.
Dabout 19 to 1 in favor of default.
Question 13
days_since_last_order (P = 0.072) and orders_per_year (P = 0.107) are not statistically significant at the 0.05 level. What is the best reading?
AThe data does not give strong evidence their true effect differs from zero in this model. That is not the same as proving the effect is exactly zero, so dropping the weaker one while keeping or re-testing the borderline one is a defensible call.
BTheir effect is proven to be exactly zero, so they must be removed.
CThey are the two most important predictors in the model.
DA high P-value means the coefficient is large.
Section D - Estimating a target you cannot fully observe yet
Questions 14-16
A different analyst wants to model days_to_pay, but there is a catch: at any moment, many invoices are still open - they have not been paid yet, so their final days_to_pay is not known. Only the invoices that have already been paid have a finished number.
Question 14
The analyst computes the average days_to_pay using only the invoices that have already been paid, and ignores the open ones. That estimate of the true average will most likely be:
Atoo high, because paid invoices always take longer than open ones.
Btoo low, because the invoices that have paid so far tend to be the faster-paying ones; the slow payers are still open and are not yet counted.
Cexactly right, because open invoices do not matter.
Dimpossible to reason about without more model output.
Question 15
The few invoices that have been paid averaged 5 days to pay, but the invoices still open have an average aging of 100 days (already outstanding 100 days and counting). What does that tell you about the true average days_to_pay for the full population of invoices?
AIt is exactly 5 days, because that is what the paid invoices show.
BIt is below 5 days, because most invoices have not been paid.
CIt is well above 5 days, because the still-open invoices are already aged past 100 days and can only finish higher.
DIt cannot possibly be above 5 days.
Question 16
What is the cleanest way to describe the mistake of estimating days_to_pay only from the invoices that have already been paid?
AThe sample is too large to be reliable.
BThe sample has too many predictor columns.
CThere is nothing wrong; the paid invoices are a random sample of all invoices.
DThe completed-payment sample is biased: it systematically leaves out the slow payers, who are still open, so it is not representative of all invoices.
Section E - Read one confusion matrix
Questions 17-20
The logistic model from Section C is turned into a yes/no decision with a cutoff of 0.5: any customer with predicted probability above 0.5 is flagged "predict default." At that cutoff, on the 2,200 customers:
When this matrix is embedded in the quiz it is shown color-coded: the correct cells - true negatives and true positives - in green, and the error cells - false positives and false negatives - in red.
Question 17
The 85 accounts in the bottom-right cell were flagged "predict default" and did in fact default. What are these called?
ATrue positives.
BFalse positives.
CTrue negatives.
DFalse negatives.
Question 18
Of the 438 customers who actually defaulted (85 + 353), how many did the model miss - fail to flag - at the 0.5 cutoff?
A85.
B45.
C353.
D1,717.
Question 19
Recall (sensitivity) is 0.194. In plain words, out of every 100 customers who truly default, the model flags about how many?
Aabout 81.
Babout 19.
Cabout 65.
Dabout 82.
Question 20
Accuracy is 0.819, which sounds strong, but recall is only 0.194. Why is the high accuracy misleading here, and what is the lever to catch more defaults?
AAccuracy is computed wrong; the model is broken and should be deleted.
BThe model needs fewer rows of data to be accurate.
CRaising the cutoff above 0.5 will catch more defaults.
DDefaults are rare (~20% base rate), so a model can score about 82% accuracy by mostly predicting "no default" while still missing most real defaults. Lowering the cutoff below 0.5 flags more customers and raises recall, at the cost of more false alarms.
Points
Twenty multiple-choice questions, 5 points each, 100 points total. The questions are auto-graded in Canvas; there is one correct option per question. A worked answer key is released after the deadline.
Points by section
Section
Questions
Pts
A - Read the OLS regression output
1-5
25
B - Spot multicollinearity from a correlation matrix
6-9
20
C - Read the logistic output
10-13
20
D - Estimating a target you cannot fully observe yet
14-16
15
E - Read one confusion matrix
17-20
20
Total
100
The class AI is built into this page. Open the Ask AI panel at the bottom-right. It will read the question you are looking at and help you reason toward why an option is right - it will not hand you the letter. Use it while you study, then submit in the Canvas New Quiz.