# Statistical Learning: 3.2 Hypothesis Testing and Confidence Intervals | Summary and Q&A

8.7K views
October 7, 2022
by
Stanford Online
Statistical Learning: 3.2 Hypothesis Testing and Confidence Intervals

## TL;DR

This content provides an overview of regression analysis and hypothesis testing, explaining how to assess the slope of a predictor, interpret p-values and confidence intervals, and evaluate the overall fit of the model.

## Key Insights

• 🏆 Hypothesis testing is used to assess the significance of a relationship between variables by testing if the coefficient is zero or not.
• 😃 The t-statistic is calculated by dividing the estimated slope by the standard error and is used in hypothesis testing.
• 😃 The p-value is the probability of obtaining a t-statistic as extreme as the observed one, indicating the likelihood of rejecting the null hypothesis.
• 💁 Confidence intervals provide additional information about the effect size and direction of the relationship between variables.
• ✋ The r-squared value measures the proportion of variance explained by the predictor, with higher values indicating a stronger relationship.
• ❓ Regression analysis with multiple predictors is a more complex problem, which will be discussed in the next section.
• ❎ The overall fit of the model can be evaluated using the residual sum of squares (RSS) and the fraction of variance explained (r-squared).

## Transcript

welcome back we talked about we just finished talking about confidence intervals in the previous segment and now we'll talk about hypothesis testing which is a closely related idea we want to ask a question about a specific value of a parameter like is that coefficient zero and in statistics that's known as hypothesis testing so hypothesis testing ... Read More

### Q: What is hypothesis testing in statistics?

Hypothesis testing is a statistical test to determine if there is a relationship between variables, such as whether a coefficient is equal to zero or not. It helps to assess the significance of a predictor in a model.

### Q: How is the null hypothesis determined in hypothesis testing?

The null hypothesis assumes that there is no relationship between variables, often written as β1 = 0. The alternative hypothesis states that there is a relationship between variables, with β1 not equal to zero.

### Q: What is a t-statistic and how is it calculated?

The t-statistic is calculated by dividing the estimated slope by the standard error. It approximates a t-distribution with n-2 degrees of freedom when the null hypothesis is true. The larger the t-statistic, the more significant the relationship between variables.

### Q: How is the p-value interpreted in hypothesis testing?

The p-value is the probability of observing a t-statistic as extreme as the one obtained, assuming the null hypothesis is true. A small p-value indicates strong evidence against the null hypothesis and suggests that the relationship between variables is statistically significant.

## Summary & Key Takeaways

• Hypothesis testing is a statistical test to determine if there is a relationship between variables, specifically if the coefficient is zero or not.

• To test the null hypothesis, a t-statistic is calculated by dividing the estimated slope by the standard error.

• The p-value is the probability of obtaining a t-statistic as extreme as the one observed or more extreme if the null hypothesis is true.