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HarvardX Data Science Module 4 - Inference and Modeling

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Updated 03/2025

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Course Description

Learn inference and modeling - two of the most widely used statistical tools in data analysis.

Prerequisites

There are no prerequisites for this course

1

Parameters and Estimates

Exercise 1. Polling - expected value of S

Exercise 2. Polling - standard error of S

Exercise 3. Polling - expected value of X-bar

Exercise 4. Polling - standard error of X-bar

Exercise 5. se versus p

Exercise 6. Multiple plots of se versus p

Exercise 7. Expected value of d

Exercise 8. Standard error of d

Exercise 9. Standard error of the spread

Exercise 10. Sample size

End of Assessment

2

Introduction to Inference

Exercise 1. Sample average

Exercise 2. Distribution of errors - 1

Exercise 3. Distribution of errors - 2

Exercise 4. Average size of error

Exercise 5. Standard deviation of the spread

Exercise 6. Estimating the standard error

Exercise 7. Standard error of the estimate

Exercise 8. Plotting the standard error

Exercise 9. Distribution of X-hat

Exercise 10. Distribution of the errors

Exercise 11. Plotting the errors

Exercise 12. Estimating the probability of a specific value of X-bar

Exercise 13. Estimating the probability of a specific error size

End of Assessment

3

Confidence Intervals and p-Values

Exercise 1. Confidence interval for p

Exercise 2. Pollster results for p

Exercise 3. Comparing to actual results - p

Exercise 4. Theory of confidence intervals

Exercise 5. Confidence interval for d

Exercise 6. Pollster results for d

Exercise 7. Comparing to actual results - d

Exercise 8. Comparing to actual results by pollster

Exercise 9. Comparing to actual results by pollster - multiple polls

End of Assessment

4

Statistical Models

Exercise 1 - Heights Revisited

Exercise 2 - Sample the population of heights

Exercise 3 - Sample and Population Averages

Exercise 4 - Confidence Interval Calculation

Exercise 5 - Monte Carlo Simulation for Heights

Exercise 6 - Visualizing Polling Bias

Exercise 7 - Defining Pollster Bias

Exercise 8 - Derive Expected Value

Exercise 9 - Expected Value and Standard Error of Poll 1

Exercise 10 - Expected Value and Standard Error of Poll 2

Exercise 11 - Difference in Expected Values Between Polls

Exercise 12 - Standard Error of the Difference Between Polls

Exercise 13 - Compute the Estimates

Exercise 14 - Probability Distribution of the Spread

Exercise 15 - Calculate the 95% Confidence Interval of the Spreads

Exercise 16 - Calculate the P-value

Exercise 17 - Comparing Within-Poll and Between-Poll Variability

End of Assessment

5

Bayesian Statistics

Exercise 1 - Statistics in the Courtroom

Exercise 2 - Recalculating the SIDS Statistics

Exercise 3 - Bayes' Rule in the Courtroom

Exercise 4 - Calculate the Probability

Exercise 5 - Misuse of Statistics in the Courts

Exercise 6 - Back to Election Polls

Exercise 7 - The Prior Distribution

Exercise 8 - Estimate the Posterior Distribution

Exercise 9 - Standard Error of the Posterior Distribution

Exercise 10- Constructing a Credible Interval

Exercise 11 - Odds of Winning Florida

Exercise 12 - Change the Priors

End of Assessment

6

Election Forecasting

Exercise 1 - Confidence Intervals of Polling Data

Exercise 2 - Compare to Actual Results

Exercise 3 - Stratify by Pollster and Grade

Exercise 4 - Stratify by State

Exercise 5- Plotting Prediction Results

Exercise 6 - Predicting the Winner

Exercise 7 - Plotting Prediction Results

Exercise 8 - Plotting the Errors

Exercise 9- Plot Bias by State

Exercise 10 - Filter Error Plot

End of Assessment

7

The t-distribution

Exercise 1 - Using the t-Distribution

Exercise 2 - Plotting the t-distribution

Exercise 3 - Sampling From the Normal Distribution

Exercise 4 - Sampling from the t-Distribution

Exercise 5 - Why the t-Distribution?

End of Assessment

8

Association and Chi-Squared Tests

Exercise 1 - Comparing Proportions of Hits

Exercise 2 - Chi-squared Test

Exercise 3 - Odds Ratio Calculation

Exercise 4 - Significance

End of Assessment

HarvardX Data Science Module 4 - Inference and Modeling

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