Alan Anderson

Statistics make it possible to analyze real-world business problems with actual data so that you can determine if a marketing strategy is really working, how much a company should charge for its products, or any of a million other practical questions. The science of statistics uses regression analysis, hypothesis testing, sampling distributions, and more to ensure accurate data analysis.

You can use the Central Limit Theorem to convert a sampling distribution to a standard normal random variable. Based on the Central Limit Theorem, if you draw samples from a population that is greater than or equal to 30, then the sample mean is a normally distributed random variable. To determine probabilities for the sample meanthe standard normal tables requires you to convertto a standard normal random variable.

After you estimate the population regression line, you can check whether the regression equation makes sense by using the coefficient of determination, also known as R2 (R squared). This is used as a measure of how well the regression equation actually describes the relationship between the dependent variable (Y) and the independent variable (X).

Summary statistical measures represent the key properties of a sample or population as a single numerical value. This has the advantage of providing important information in a very compact form. It also simplifies comparing multiple samples or populations. Summary statistical measures can be divided into three types: measures of central tendency, measures of central dispersion, and measures of association.

Before you apply statistical techniques to a dataset, it's important to examine the data to understand its basic properties. You can use a series of techniques that are collectively known as Exploratory Data Analysis (EDA) to analyze a dataset. EDA helps ensure that you choose the correct statistical techniques to analyze and forecast the data.

Compared with other types of hypothesis tests, constructing the test statistic for ANOVA is quite complex. The first step in finding the test statistic is to calculate the error sum of squares (SSE). Calculating the SSE enables you to calculate the treatment sum of squares (SSTR) and total sum of squares (SST).

Regression analysis is used to estimate the strength and direction of the relationship between variables that are linearly related to each other. Two variables X and Y are said to be linearly related if the relationship between them can be written in the form Y = mX + b where m is the slope, or the change in Y due to a given change in X b is the intercept, or the value of Y when X = 0 As an example of regression analysis, suppose a corporation wants to determine whether its advertising expenditures are actually increasing profits, and if so, by how much.

One technique you can use to identify the distribution a dataset follows is the QQ-plot (QQ stands for quantile-quantile). You can use the QQ-plot to compare a dataset to a large number of different probability distributions. Often, data is compared to the normal distribution because many statistical tests assume normally distributed data.

Prior to performing any type of statistical analysis, understanding the nature of the data being analyzed is essential. You can use EDA to identify the properties of a dataset to determine the most appropriate statistical methods to apply to the data. You can investigate several types of properties with EDA techniques, including the following: The center of the data The spread among the members of the data The skewness of the data The probability distribution the data follows The correlation among the elements in the dataset Whether or not the parameters of the data are constant over time The presence of outliers in the data Another key question EDA answers is "Does the data conform to our assumptions?