Evaluation Metrics for ML Models

• Accuracy: The ratio of correctly predicted instances.

• Precision: Correct positive predictions divided by total predicted positives.

• Recall: Correct positive predictions divided by actual positives.

• F1 Score: The harmonic mean of precision and recall.

  

K-Nearest Neighbors (KNN) Algorithm

• A classification algorithm that works by finding the 'k' closest training examples to a data point.

• Strengths: Simple to understand, effective for smaller datasets.

• Weaknesses: Sensitive to irrelevant features and the scale of the data.

• Applications: Image recognition, recommendation systems.

Ensemble Learning Techniques

• Combines multiple models to improve predictive performance.

• Methods:

  • Bagging (e.g., Random Forests)
  • Boosting (e.g., AdaBoost)

Creating a comprehensive cheat sheet for statistical analysis in a Bachelor of Technology (BTech) program involves covering a wide range of topics and formulas. Below is a condensed version of this essential reference:

Descriptive Statistics

Measures of Central Tendency

• Mean: \(\bar{x} = \frac{\sum{x}}{n}\)
• Median: Depends on data arrangement.
• Mode: Most frequent value.

Measures of Dispersion

• Variance: \(s^2 = \frac{\sum(x - \bar{x})^2}{n-1}\)
• Standard Deviation: \(s = \sqrt{s^2}\)
• Range: \(Range = Max(x) - Min(x)\)
• Interquartile Range (IQR): \(Q3 - Q1\)

Measures of Shape

• Skewness
• Kurtosis

Probability

Basic Probability

• \(P(A)\) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
• \(P(A \cup B)\) = \(P(A) + P(B) - P(A \cap B)\)

Conditional

Operations Management Key Concepts

Inventory Management & Production Planning

• Final Inventories Analysis

  Final inventories for the last 4 months: FI = S(100) O(120) N(-130) D(430). Response: O(2750) N(1400) D(3750).

• Production Strategy Aggregation

  Which production strategy aggregates production? Response: Strategy to adjust demand.

• Production Planning Metrics

  Number of Products (N.Prod) = 10,000 units | Production Days = 20 | Workforce = 43. Response: 459 units.

• Actuation Possibilities

  Actuation possibilities: Demand/Capacity. Response: Actuation/Aggressive.

• Lot-for-Lot (LFL) Parameters

  LFL parameters: Ts2 Av25 Ss10 Level0 RefP3.

• Gross Requirements Calculation

  Gross Requirements: (0.50, 0.100, 0.75, 0.80, 0.90, 0.100). Response: (0.100, 0.70, 0.70,

Surveying Measurement Accuracy and Error Propagation

Tolerance should be imposed only by the requirements of the research. It should be conditional on the surveying instrument used for this tolerance; it would be naive to expect very great accuracy using a blunt instrument.

Transmission Error (Mean Square Error of a Sum)

The mean square error (MSE) of a sum is equal to the square root of the sum of the squares of the mean square errors of the summands, provided the measurements are made with different precision. If measurements are performed with equal precision, it can be shown that the mean square error is the same for all addends.

Exercises

1. Six measures of the length of a building's facade were made using a steel tape (listed in the table...

Exercise 1: Calculating Monthly Interest Rate

A person invested $12,000 in an institution and received $13,008.00 after seven months. What is the equivalent monthly interest rate that the investor earned?

Solution:

• Initial Capital (C) = $12,000
• Time (n) = 7 months
• Future Value (FV) = $13,008.00

Using the formula: FV / C = (1 + i * n)

13,008.00 / 12,000.00 = (1 + i * 7)

1. 0840 = 1 + 7i

2. 0840 = 7i

i = 0.0840 / 7

i = 0.012 or 1.2% per month

Exercise 2: Equivalent Financial Return

An investment of $15,000 is made for a period of three months at a simple interest rate of 26% per annum. What amount must be invested for two months at a linear rate of 18% per year to achieve the same financial return?

Solution:

Investment 1:

• C = $15,000
• n = 3 months
• i (annual)

1. New Followers

Formula: New followers = Final followers - Initial followers

Use it when: The case provides follower counts at the beginning and end of the year.

Meaning: Indicates the total number of new followers generated by the campaign.

2. Cost per New Follower

Formula: Cost per new follower = Campaign cost / New followers

Meaning: Shows the acquisition cost for a single new follower.

Interpretation: A lower cost per follower indicates higher campaign efficiency.

3. New Customers from Followers

Formula: New customers = New followers × Conversion rate

Meaning: Calculates how many followers converted into actual customers.

4. Customer Acquisition Cost (CAC)

Formula: CAC = Campaign cost / New customers

Interpretation: A lower CAC is preferred as it...

Quick Graph Identification

• Holes: Represented by open circles.
• Vertical Asymptotes: Represented by dashed vertical lines.
• Horizontal or Slant Asymptotes: Represented by dashed lines.
• Note: The graph approaches but never touches the asymptotes.

Understanding Domain

• Exclude values that make the denominator equal to zero.
• Even if a factor cancels, the value is still excluded from the domain.

Example: (x + 3) / (x(x + 3))
Domain: x ≠ -3, x ≠ 0

Final One-Pass Checklist

1. Factor and cancel.
2. Find holes.
3. Find vertical asymptotes.
4. Find x-intercepts.
5. Find the y-intercept.
6. Find horizontal or slant asymptotes.

Exponential and Logarithmic Functions

Exponential: f(x) = a · b^(x - h) + k (where b > 0, b ≠ 1)
Logarithmic: f(x) = a · log_b(x - h) + k
Note: Logarithms...

Corporate Distribution Layers

Distributions are applied in the following order: Accumulated E&P + Current E&P, then basis, then the remainder is treated as capital gain.

• No Dividend: If there is no E&P, reduce current E&P first. Negative AEP still distributes E&P.
• Offset: Half of current E&P is lost to offset AEP before distribution.

Property Distributions

Recognize gains, but not losses.

• Dividend: FMV - Liabilities
• Basis: FMV
• Gains: FMV - Tax Basis

Distribution Table

The amount from CEP is calculated as: (Period distribution / Total distribution) * CEP. AEP is applied to the remainder, then to stock basis.

Stock Distributions and Redemptions

• Stock Distribution: Proportionate distributions are nontaxable and do not reduce E&