Descriptive statistics summarize and describe data through measures like mean, median, range, and standard deviation. Inferential statistics make inferences about an unknown population based on a sample, using methods like estimation, hypothesis testing, and regression. Regression finds the linear relationship between variables to estimate a dependent variable's value given an independent variable. It should only be used if there is significant linear correlation and the independent variable values are close to the original data.

1. Descriptive statistics Definition: Descriptive statistics refers to statistical techniques used to summarise and describe a data set, and also to the statistics (measures) used in such summaries. Measures of central tendency, such as mean and median , and dispersion, such as range and standard deviation , are the main descriptive statistics. Displays of data , such as histograms and box-plots , are also considered techniques of descriptive statistics.

2. Inferential statistics Definition: Inferential statistics, or statistical induction, means the use of statistics to make inferences concerning some unknown aspect of a population from a sample of that population. A common method used in inferential statistics is estimation. In estimation, the sample is used to estimate a parameter , and a confidence interval about the estimate is constructed. Other examples of inferential statistics methods include hypothesis testing , linear regression , and principle components analysis .

3. The difference between them There are two fundamental purposes to analyzing data: the first is to describe a large number of data points in a concise way by means of one or more summary statistics; the second is to draw inferences about the characteristics of a population based on the characteristics of a sample. Descriptive statistics characterize the distribution of a set of observations on a specific variable or variables. By conveying the essential properties of the aggregation of many different observations, these summary measures make it possible to understand the phenomenon under study better and more quickly than would be possible by studying a multitude of unprocessed individual values. Inferential statistics allow one to draw conclusions about the unknown parameters of a population based on statistics which describe a sample from that population. Very often, mere description of a set of observations in a sample is not the goal of research. The data on hand are usually only a sample of the actual population of interest, possibly a minute sample of the population. For example, most presidential election polls only sample about 1,000 individuals, and yet the goal is to describe the expected voting behavior of 100 million or more potential voters.

4. Regression Definition: The idea behind regression is that when there is significant linear correlation, you can use a line to estimate the value of the dependent variable for certain values of the independent variable. The regression equation should only used: When there is significant linear correlation. That is, when you reject the null hypothesis that rho=0 in a correlation hypothesis test. The value of the independent variable being used in the estimation is close to the original values. That is, you should not use a regression equation obtained using x's between 10 and 20 to estimate y when x is 200. The regression equation should not be used with different populations. That is, if x is the height of a male, and y is the weight of a male, then you shouldn't use the regression equation to estimate the weight of a female. The regression equation shouldn't be used to forecast values not from that time frame. If data is from the 1960's, it probably isn't valid in the 1990's.

5. Regression formula a is the slope of the regression line: b is the y-intercept of the regression line: The regression line is sometimes called ‘’the line of best fit’’ or ‘’the best fit line’’ Since it "best fits" the data, it makes sense that the line passes through the means. The regression equation is the line with slope a passing through the point Another way to write the equation would be: