The rate parameter (lambda) in a Poisson distribution determines the average rate of occurrence per interval, which directly affects the shape of the distribution. Higher lambda values result in distributions that are less skewed to the right.

The null hypothesis is a statement in statistical inference which asserts that there is no significant difference between the set of observed and expected data.

Spearman's Rank Correlation is less sensitive to outliers than Pearson's correlation. This is because Spearman's correlation is based on rank orders rather than raw data values, making it more robust against outliers.

The Chi-square test for goodness of fit is used when we have categorical data and we want to see if the data follows a specific distribution.

A Type I error in hypothesis testing is the incorrect rejection of a true null hypothesis, often signified by the Greek letter alpha (α). In other words, a Type I error happens when the researcher incorrectly concludes that the null hypothesis is false when, in fact, it is true.

Outliers can significantly distort the principal components identified by PCA, as they can artificially inflate the variance along their direction. It's generally a good practice to address outliers before applying PCA.

No, PCA is a technique for unsupervised learning. It does not use any class label information in its algorithm, making it unsupervised. However, the transformed dataset from PCA can be used for subsequent supervised learning tasks.

A residual plot shows the residuals on the y-axis and the independent variable on the x-axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

ANOVA stands for Analysis of Variance. It is a statistical method used to compare the means of two or more groups.

Bayes' theorem is a principle in probability theory and statistics that describes how to update the probabilities of hypotheses (prior probabilities) when given evidence (new data).

Outliers can have a significant impact on the skewness of a distribution. An outlier can increase skewness if it is further from the mean in the direction of the skew. Conversely, an outlier can decrease skewness if it is further from the mean in the direction opposite to the skew. The extent of the impact depends on the value and direction of the outlier relative to the rest of the data.

K-means is a popular method for cluster analysis that partitions the data into non-hierarchical clusters. The algorithm iteratively assigns each data point to one of the K clusters based on the feature similarity (distance).