In a Chi-square test for goodness of fit, the degrees of freedom are calculated as the number of categories minus one. This reflects the number of values in the final calculation that are free to vary.

The choice of bin size in a histogram can greatly affect the resulting visualization. If the bins are too large, important features of the data may be obscured. If the bins are too small, the histogram may appear too 'noisy' and it may be difficult to interpret underlying patterns. Thus, the choice of bin size can indeed change the perceived shape of the histogram.

Heteroscedasticity can be resolved by transforming the dependent variable, typically using a logarithmic transformation. This often stabilizes the variance of the residuals across different levels of the predictors.

A Poisson distribution is used when we are counting the number of times an event happens over a fixed interval of time or space, and the events are independent and occur at a constant average rate. It's often used to model random events such as calls to a call center or arrivals at a website.

Qualitative data can be transformed into quantitative data for analysis by coding the responses. This is a process where categories or themes identified in the qualitative data are assigned numerical codes. These numerical codes can then be used in statistical analyses. For instance, if you have data on types of pets (dogs, cats, etc.), you can assign a numerical code (1 for dogs, 2 for cats, etc.) to transform this qualitative data into quantitative data.

K-means clustering requires the number of clusters to be defined beforehand, while hierarchical clustering does not. Hierarchical clustering forms a dendrogram from which the user can choose the number of clusters based on the problem requirements.

Multicollinearity refers to a high correlation among independent variables in a regression model. It does not reduce the predictive power or reliability of the model as a whole, but it can cause instability in the estimation of individual regression coefficients, making them difficult to interpret.

The sampling distribution in statistics is the probability distribution of a given statistic based on a random sample. For a statistic that is calculated from a sample, each different sample could (and likely will) provide a different value of that statistic. The sampling distribution shows us how those calculated statistics would be distributed.

The binomial distribution approaches the normal distribution as the number of trials gets large, provided that the probability of success is not too close to 0 or 1. This is known as the De Moivre–Laplace theorem.

Inference in multiple linear regression primarily involves interpreting the coefficients of the model, which represent the expected change in the response variable for each one-unit change in the respective explanatory variable, assuming all other variables are held constant.