Even in the presence of multicollinearity, the least squares estimates of the regression coefficients are still unbiased. However, they are less precise and have high standard errors.

The standard deviation and mean absolute deviation both measure the dispersion in a dataset. The key difference lies in how they treat deviations from the mean: standard deviation squares the deviations before averaging them, while mean absolute deviation takes the absolute value of deviations before averaging. As a result, standard deviation is more sensitive to extreme values than the mean absolute deviation.

Quantitative data represents quantities and can be measured on a Numerical scale. It includes both discrete data (e.g., the number of students in a class) and continuous data (e.g., the weight of a person).

Pearson's correlation coefficient (denoted as r) is a measure of the strength and direction of association that exists between two continuous variables. It measures the degree to which pairs of data for these two variables lie on a line. The values lie between -1 and 1, where 1 indicates a perfect positive correlation, -1 a perfect negative correlation, and 0 no correlation at all.

If the population standard deviation is unknown, the sample standard deviation is used to estimate the standard error of the mean. The standard error is a measure of how much the sample mean is expected to vary from the true population mean.

If the F statistic in an ANOVA is significantly high, it suggests that the null hypothesis should be rejected. The null hypothesis in ANOVA is typically that all group means are equal.

The Chi-square test for goodness of fit is applicable only to categorical data. It is used to determine whether the observed frequencies differ from the expected frequencies.

The Law of Large Numbers and the Central Limit Theorem are both key concepts in probability and statistics, but they say different things. The Law of Large Numbers states that as the size of a sample is increased, the sample mean will get closer to the population mean. The Central Limit Theorem, on the other hand, states that as the sample size increases, the distribution of sample means approaches a normal distribution.

This is known as an interaction effect. In the context of regression analysis, an interaction effect occurs when the effect of one independent variable on the dependent variable depends on the value of another independent variable.

The total probability of all outcomes of an experiment is 1. This is a fundamental rule of probability, known as the Law of Total Probability, which states that the sum of the probabilities of all possible outcomes of an experiment is equal to 1.