This unit explains the importance of statistical methods in analyzing and interpreting data in data science. It covers descriptive statistics to summarize data and probability concepts to model uncertainty. Inferential statistics, including sampling, hypothesis testing, confidence intervals, and regression analysis, are used to draw conclusions about populations from sample data

1. Unit 3: Statistical Methods in
Data Science
Probability, Statistics, Correlation,
and Regression
Your name, date, course, institution

2. Introduction
• Role of statistics in data science
• Helps in making data-driven decisions
• Key areas: probability, inference, correlation,
regression

3. Probability Theory Basics
• Definition: Likelihood of an event occurring
• Types of probability:
– Classical, Empirical, Subjective
• Events: independent vs dependent, mutually
exclusive

4. Probability Rules
• Addition Rule: P(A B)=P(A)+P(B)
∪
−P(A∩B)P(A cup B) = P(A) + P(B) - P(A
cap B)P(A B)=P(A)+P(B)−P(A∩B)
∪
• Multiplication Rule:
P(A∩B)=P(A) P(B A)P(A cap B) = P(A)
⋅ ∣
cdot P(B|A)P(A∩B)=P(A) P(B A)
⋅ ∣
• Complement Rule: P(A′)=1−P(A)P(A') = 1 -
P(A)P(A′)=1−P(A)

5. Random Variables and Distributions
• Random Variables: Quantitative outcome of
experiments
• Types: Discrete (e.g., dice), Continuous (e.g.,
height)
• Common distributions: Normal, Binomial,
Poisson

6. Inferential Statistics
• Use sample data to make population-level
conclusions
• Two key concepts:
– Estimation (point and interval)
– Hypothesis testing

7. Hypothesis Testing
• Steps:
– Null hypothesis (H0H_0H0​
) vs alternative
(H1H_1H1​
)
– Choose significance level (αalphaα)
– Compute test statistic
– Compare with critical value / p-value
• Types: t-test, chi-square, ANOVA

8. p-values
• Definition: Probability of observing results as
extreme as the sample, assuming H0H_0H0​is
true
• Interpretation:
– p < 0.05 → reject H0H_0H0​
– p ≥ 0.05 → fail to reject H0H_0H0​

9. Confidence Intervals
• Range of plausible values for a population
parameter
• Example: 95% CI → we are 95% confident the
true mean lies within this interval
• Formula (for mean): xˉ±Zα/2 σ
⋅ nbar{x} pm
Z_{alpha/2} cdot frac{sigma}{
sqrt{n}}xˉ±Zα/2​
⋅n​
σ​

10. Correlation
• Measures the strength and direction of a linear
relationship between two variables
• Correlation coefficient (r):
– r = 1 → perfect positive
– r = -1 → perfect negative
– r = 0 → no linear correlation

11. Causality vs Correlation
• Correlation ≠ Causation
• Causal inference requires experimental design
or advanced methods (e.g., regression, A/B
testing)
• Important to avoid misleading conclusions

12. Introduction to Linear Regression
• Predicts a dependent variable (Y) from one
or more independent variables (X)
• Simple linear regression formula:
Y=β0+β1X+ϵY = beta_0 + beta_1 X +
epsilonY=β0​
+β1​
X+ϵ

13. Statistical Foundations of Regression
• Assumptions: Linearity, independence,
homoscedasticity, normality of errors
• Interpretation of coefficients:
– β0beta_0β0​→ intercept
– β1beta_1β1​→ change in Y for 1 unit change in X
• Goodness of fit: R2R^2R2

14. Hypothesis Testing in Regression
• Test if predictor variables significantly affect
Y
• Null hypothesis: βi=0beta_i = 0βi​
=0
• p-value from t-test → determines significance

15. Summary
• Probability theory underpins statistical
inference
• Inferential statistics allows decision-making
with uncertainty
• Correlation identifies relationships; regression
quantifies and predicts
• Proper statistical methods ensure reliable data-
driven insights

16. Thank You