Linear regression is widely used to model the relationship between response or dependent variable and explanatory or independent variables. The parameter in the model has linear form. When there is only one explanatory assumed in the model, it is called simple linear regression.
When we do data analysis, random variables in the dataset are usually mutually correlated. Sometimes, we may want to measure the pure relationship between two variables, and the influence from other variables being controlled. A partial correlation calculation could fulfill this purpose.
When a correlation, usually Person type correlation, is calculated, two variables have to be continuous. But this requirement does not excludes the situation when one of the two variables is a dichotomous (binary) distributed. Say if we want to measure the correlations between height and gender for a group of people, the variable gender has clear dichotomous values. This kind of Pearson correlation is called point-biserial correlation, because the value for gender variable is strictly 0 or 1.
dplyr is a package that belongs to tidyverse framework. dplyr allows usage of pipeline structure (%>%), which can chain multiple functions together into one statement to make data management more effective. spread() of dplyr is a function that spreads the values of columns from the current data frame, and make them as column labels in the resulting data frame.
R language provides several useful functions for importing delimited files and creating data frames. These delimited files are often stored in local computer directory, with extensions ‘txt’, ‘csv’, ‘dat’. The mostly widely used functions for importing these files in R are read.table() and read.csv().
Categorical variables, including nominal and ordinal variables in R programming language are called factor variables. For example, gender(male/female) is nominal, and survey results (excellent, good, normal, bad) have ordinal values. Categorical variables are useful because many data analysis operations are related to values in different categories, such as contingency tables between two categorical variables for independence analysis, hypothesis testing of homogeneity of variances, just name a few.
list is a type of data structure in R programming language. Unlike other data structures, especially matrix and vector, in which each element must has the same type of data, a list provides the flexibility of storing various information in one object.
Violin plot is quite similar as boxplot, in the sense that it shows the range of the data. And at the same time a violin plot illustrates the data distribution shape with a density curve on both sides of the central pillar.
A Student t-distributed random variable is modeling the ratio between a standard Normal random variate and square root of a Chi-squared random variable divided by its degrees of freedom.
Kernel density function is a nonparametric method to find the drawing density curve of random samples, and it is often used to draw a smoothed curve in data visualization. In R programming with ggplot2 package, a chaining of functions ggplot() and geom_density() is often used to draw different smoothed curves showing the distribution of continuous variables.