Data Science Topic 11: Chi-Squared and Regression Tests

A set of vocabulary flashcards covering Topic 11 of Data Science, focusing on Chi-Squared Goodness of Fit, Independence tests, Regression Slope tests, and their associated assumptions and R implementation.

🤔 Who's the genius behind the Chi-Squared Test?

Karl Pearson invented this test in 1900. K for Karl, P for Pearson - they’re like the ultimate dynamic duo! 🍇

💡 What does the $\chi^2$ Formula do?

It checks how observed counts differ from expected ones: $\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}$. Think of it like a matchmaker assessing if reality matches expectations! 💞

🌈 What type of distribution is the $\chi^2$ Distribution?

It's a right-tailed distribution that starts at zero, showcasing only positive values. Visualize it as a party that welcomes only guests on the right side! 🚪➡️

🎲 What does the $\chi^2$ Goodness of Fit test?

It checks if one qualitative variable fits a theoretical distribution—like testing if a die is truly fair. Kind of like making sure you didn’t roll a double six too often! 🎲✨

📏 What's Cochran's Rule in Chi-Squared?

It states that all expected frequencies must be $> 0$, and no more than $20\%$ can be $< 5$. Imagine baking cookies; they must all have enough dough to be yummy! 🍪

🍦 How do you calculate Degrees of Freedom for Goodness of Fit?

It's $k - 1$, where $k$ is the number of categories. Imagine counting ice cream flavors but leaving one out for your base flavor! 🍦

🧦 What does the $\chi^2$ Test for Independence check?

It assesses if two qualitative variables are related or independent. Think of it as examining whether wearing socks with sandals affects your coolness factor! 🧦👡

🎂 How to calculate Degrees of Freedom for the Independence Test?

It's $(m - 1)(n - 1)$, with $m$ being rows and $n$ columns. Picture stacking cake layers that must support each other! 🍰

🍕 How is Expected Frequency calculated for Independence?

It's given by $Expected = \frac{Row Total \times Column Total}{Grand Total}$. Imagine cutting a pizza based on your party guests; everyone deserves a slice! 🍕

🚦 What does a Mosaic Plot show us?

It visualizes observation comparisons with blue for more than expected and red for fewer; like a data traffic light! 🚦🎨

🎯 What does the Regression Test for Slope evaluate?

It’s a t-test to check if a slope is significant, akin to testing your accuracy in a dart game! Are you hitting the bullseye? 🎯

🔮 What does $H_0$ stand for in Regression Slope?

It’s the null hypothesis saying $\beta_1 = 0$, meaning there’s no relationship. Think of it as stating, 'No magic here!' ✨🚫

✂️ How to calculate Degrees of Freedom for Regression?

It’s simply $n - 2$ where $n$ is total observations. Trim the extra to find that best-fitting line! ✂️📏

🏆 What does $T$ (Test Statistic) tell us?

Calculated as $T = \frac{\hat{\beta}_1}{SE(\hat{\beta}_1)}$, it finds out how big the slope is compared to its standard error—like taking a victory lap after scoring big! 🏃‍♂️🏆

🎉 What is Homoscedasticity in regression?

This means residuals scatter randomly without patterns. Imagine tossing confetti everywhere—nice and even! 🎉

✈️ How do we check the Normality of Residuals?

Use a QQ plot to see if points stick close to the diagonal line; think of aiming your paper airplane for accuracy! ✈️📏

👩‍🍳 What function does chisq.test() perform in R?

It carries out chi-squared tests with a count table or matrix. Picture R as your personal statistics chef cooking up hypotheses! 👩‍🍳📊

👑 What does retaining $H_0$ signify?

It indicates $p > \alpha$, which means there's not enough evidence to reject the null. You’re winning the debate and keeping your crown! 👑

🎆 What happens when we reject $H_0$?

It means $p < \alpha$, revealing strong evidence against the null. Imagine setting off fireworks after proving your point! 🎆

🚗 What is the Linearity Assumption in regression?

This requires that the scatterplot looks linear—no curves allowed. Think of it like driving straight along the highway, no turns! 🚗💨