Bivariate Analysis

Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis.It involves the analysis of two variables(often denoted asX,Y), for the purpose of determining the empirical relationship between them

Bivariate analysis can be helpful in testing simple hypotheses of association. Bivariate analysis can help determine to what extent it becomes easier to know and predict a value for one variable (possibly a dependent variable) if we know the value of the other variable (possibly the independent variable) (see also correlation and simple linear regression). Bivariate analysis can be contrasted with univariate analysis in which only one variable is analysed.Like univariate analysis, bivariate analysis can be descriptive or inferential. It is the analysis of the relationship between the two variables.Bivariate analysis is a simple (two variable) special case of multivariate analysis(where multiple relations between multiple variables are examined simultaneously).

Waiting time between eruptions and the duration of the eruption for the Old Faithful Geyser in Yellowstone National Park, Wyoming, USA. This scatterplot suggests there are generally two "types" of eruptions: short-wait-short-duration, and long-wait-long-duration.

Graphical Methods

Graphs that are appropriate for bivariate analysis depend on the type of variable. For two continuous variables, a scatterplot is a common graph. When one variable is categorical and the other continuous, a box plot is common and when both are categorical a mosaic plot is common. These graphs are part of descriptive statistics.

Questions

Suppose we have two random variables, X and Y, which are bivariate normal. The correlation between them is -0.2. Let A = cX + Y and B = X + cY. For what values of c are A and B independent? https://en.wikipedia.org/wiki/Bivariate_analysis