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.

To estimate a time series regression model, a trend must be estimated. You begin by creating a line chart of the time series. The line chart shows how a variable changes over time; it can be used to inspect the characteristics of the data, in particular, to see whether a trend exists. For example, suppose you're a portfolio manager and you have reason to believe a linear trend occurs in a time series of returns to Microsoft stock.

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).

A histogram is a graph that represents the probability distribution of a dataset. A histogram has a series of vertical bars where each bar represents a single value or a range of values for a variable. The heights of the bars indicate the frequencies or probabilities for the different values or ranges of values.

A quantile-quantile plot (also known as a QQ-plot) is another way you can determine whether a dataset matches a specified probability distribution. QQ-plots are often used to determine whether a dataset is normally distributed. Graphically, the QQ-plot is very different from a histogram. As the name suggests, the horizontal and vertical axes of a QQ-plot are used to show quantiles.

Regression analysis is a statistical tool used for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another — the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate.