Higher variability in the population increases the width of the confidence interval. When data points are spread out more (higher variability), there is more uncertainty about where the true population parameter lies, leading to a larger standard error and thus a wider confidence interval.

Correlation occurs when changes in one variable are associated with changes in another variable. It's important to remember that correlation does not imply causation. Just because two variables move together, it does not mean that one variable's movement is causing the other's.

The Breusch-Pagan test checks for heteroscedasticity by regressing the squared residuals on the predictors. If the predictors explain a significant amount of variance in the squared residuals, the test concludes that heteroscedasticity is present.

The 'whiskers' in a box plot represent the range of the data. The upper whisker extends to the maximum data value or up to 1.5 times the interquartile range (IQR), while the lower whisker extends to the minimum data value or up to 1.5 times the IQR. Any data points beyond the whiskers can be considered outliers.

The assumption of IID residuals is important because it ensures that standard errors, confidence intervals, and hypothesis tests are valid. If this assumption is violated, these statistics may be incorrect, leading to misleading results.

The median is preferred over the mean when our data is skewed or has outliers. Outliers can greatly affect the mean and create a distorted view of the data, but the median is not affected by outliers or skewed data. The median is the middle score for a set of data that has been arranged in order of magnitude, making it a better measure when dealing with skewed distributions.

Discrete random variables are variables that can only take on a countable number of values, such as integers, while continuous random variables can take on any value within a certain range or interval.

A distribution with positive skewness is said to be positively skewed or right-skewed, which means it has a long tail in the positive direction on the number line.

The null hypothesis in an ANOVA test is that the means of all groups are equal. If the p-value obtained from the ANOVA test is less than the significance level, the null hypothesis is rejected, implying that there is a significant difference between at least two of the group means.

In a scatter plot, an upward trend suggests a positive relationship between the variables. This means as one variable increases, the other variable also increases.

In factor analysis, eigenvalues represent the total variance explained by each factor. A larger eigenvalue indicates that more of the total variance is accounted for by that factor.

Pearson's Correlation Coefficient assumes that the variables are normally distributed. It's one of the key assumptions made when calculating the coefficient, and it refers to the shape of the distribution of the values.