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# HarvardX Data Science Module 4 - Inference and Modeling

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## Course Description

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

- 1
### Parameters and Estimates

**Free**In this chapter, you will learn about parameters and estimates using the example of election polling.

Exercise 1. Polling - expected value of S50 xpExercise 2. Polling - standard error of S50 xpExercise 3. Polling - expected value of X-bar50 xpExercise 4. Polling - standard error of X-bar50 xpExercise 5. se versus p100 xpExercise 6. Multiple plots of se versus p100 xpExercise 7. Expected value of d50 xpExercise 8. Standard error of d50 xpExercise 9. Standard error of the spread100 xpExercise 10. Sample size50 xpEnd of Assessment50 xp - 2
### Introduction to Inference

**Free**In this chapter, you will learn about the central limit theorem in practice.

Exercise 1. Sample average100 xpExercise 2. Distribution of errors - 1100 xpExercise 3. Distribution of errors - 250 xpExercise 4. Average size of error100 xpExercise 5. Standard deviation of the spread100 xpExercise 6. Estimating the standard error100 xpExercise 7. Standard error of the estimate100 xpExercise 8. Plotting the standard error50 xpExercise 9. Distribution of X-hat50 xpExercise 10. Distribution of the errors50 xpExercise 11. Plotting the errors100 xpExercise 12. Estimating the probability of a specific value of X-bar100 xpExercise 13. Estimating the probability of a specific error size100 xpEnd of Assessment50 xp - 3
### Confidence Intervals and p-Values

**Free**In this chapter, you will learn about confidence intervals and p-values using actual polls from the 2016 US Presidential election.

Exercise 1. Confidence interval for p100 xpExercise 2. Pollster results for p100 xpExercise 3. Comparing to actual results - p100 xpExercise 4. Theory of confidence intervals50 xpExercise 5. Confidence interval for d100 xpExercise 6. Pollster results for d100 xpExercise 7. Comparing to actual results - d100 xpExercise 8. Comparing to actual results by pollster100 xpExercise 9. Comparing to actual results by pollster - multiple polls100 xpEnd of Assessment50 xp - 4
### Statistical Models

**Free**In this chapter, you will learn about different types of probability models

Exercise 1 - Heights Revisited100 xpExercise 2 - Sample the population of heights100 xpExercise 3 - Sample and Population Averages50 xpExercise 4 - Confidence Interval Calculation100 xpExercise 5 - Monte Carlo Simulation for Heights100 xpExercise 6 - Visualizing Polling Bias100 xpExercise 7 - Defining Pollster Bias50 xpExercise 8 - Derive Expected Value50 xpExercise 9 - Expected Value and Standard Error of Poll 150 xpExercise 10 - Expected Value and Standard Error of Poll 250 xpExercise 11 - Difference in Expected Values Between Polls50 xpExercise 12 - Standard Error of the Difference Between Polls50 xpExercise 13 - Compute the Estimates100 xpExercise 14 - Probability Distribution of the Spread50 xpExercise 15 - Calculate the 95% Confidence Interval of the Spreads100 xpExercise 16 - Calculate the P-value100 xpExercise 17 - Comparing Within-Poll and Between-Poll Variability100 xpEnd of Assessment50 xp - 5
### Bayesian Statistics

**Free**In this chapter, you will learn about Bayesian statistics.

Exercise 1 - Statistics in the Courtroom50 xpExercise 2 - Recalculating the SIDS Statistics100 xpExercise 3 - Bayes' Rule in the Courtroom50 xpExercise 4 - Calculate the Probability100 xpExercise 5 - Misuse of Statistics in the Courts50 xpExercise 6 - Back to Election Polls100 xpExercise 7 - The Prior Distribution50 xpExercise 8 - Estimate the Posterior Distribution100 xpExercise 9 - Standard Error of the Posterior Distribution100 xpExercise 10- Constructing a Credible Interval100 xpExercise 11 - Odds of Winning Florida100 xpExercise 12 - Change the Priors100 xpEnd of Assessment50 xp - 6
### Election Forecasting

**Free**In this chapter, you will learn about election forecasting by exploring data from the 2016 US Presidential Election.

Exercise 1 - Confidence Intervals of Polling Data100 xpExercise 2 - Compare to Actual Results100 xpExercise 3 - Stratify by Pollster and Grade100 xpExercise 4 - Stratify by State100 xpExercise 5- Plotting Prediction Results100 xpExercise 6 - Predicting the Winner100 xpExercise 7 - Plotting Prediction Results100 xpExercise 8 - Plotting the Errors100 xpExercise 9- Plot Bias by State100 xpExercise 10 - Filter Error Plot100 xpEnd of Assessment50 xp - 7
### The t-distribution

**Free**In this chapter, you will learn about the t-distribution.

- 8
### Association and Chi-Squared Tests

**Free**In this chapter, you will learn about the association tests and the chi-square test.

Datasets

Readme#### Weston Stearns

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