H@ZIQ: Excel

Microsoft Excel is a spreadsheet program which allows one to enter numerical values or data into the rows or columns of a spreadsheet, and to use these numerical entries for such things as calculations, graphs, and statistical analysis.

Microsoft Excel has the basic features of all spreadsheets, using a grid of cells arranged in numbered rows and letter-named columns to organize data manipulations like arithmetic operations. It has a battery of supplied functions to answer statistical, engineering and financial needs. In addition, it can display data as line graphs, histograms and charts, and with a very limited three-dimensional graphical display. It allows sectioning of data to view its dependencies on various factors from different perspectives (using pivot tables and the scenario manager). And it has a programming aspect, Visual Basic for Applications, allowing the user to employ a wide variety of numerical methods, for example, for solving differential equations of mathematical physics, and then reporting the results back to the spreadsheet. Finally, it has a variety of interactive features allowing user interfaces that can completely hide the spreadsheet from the user, so the spreadsheet presents itself as a so-called application, or decision support system (DSS), via a custom-designed user interface, for example, a stock analyzer, or in general, as a design tool that asks the user questions and provides answers and reports. In a more elaborate realization, an Excel application can automatically poll external databases and measuring instruments using an update schedule, analyze the results, make a Word report or Power Point slide show, and e-mail these presentations on a regular basis to a list of participants.

Microsoft allows for a number of optional command-line switches to control the manner in which Excel starts.

Linear Regression

Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data. In some situations, the slope and/or intercept have a scientific meaning. In other cases, you use the linear regression line as a standard curve to find new values of X from Y, or Y from X.

The term "regression", like many statistical terms, is used in statistics quite differently than it is used in other contexts. The method was first used to examine the relationship between the heights of fathers and sons. The two were related, of course, but the slope is less than 1.0. A tall father tended to have sons shorter than himself; a short father tended to have sons taller than himself. The height of sons regressed to the mean. The term "regression" is now used for many sorts of curve fitting.

Prism determines and graphs the best-fit linear regression line, optionally including a 95% confidence interval or 95% prediction interval bands. You may also force the line through a particular point (usually the origin), calculate residuals, calculate a runs test, or compare the slopes and intercepts of two or more regression lines.

In general, the goal of linear regression is to find the line that best predicts Y from X. Linear regression does this by finding the line that minimizes the sum of the squares of the vertical distances of the points from the line.

Note that linear regression does not test whether your data are linear (except via the runs test). It assumes that your data are linear, and finds the slope and intercept that make a straight line best fit your data.

Quadratic Regression

Quadratic Regression is a process by which the equation of a parabola is found that “best fits” a given set of data. Quadratic regression models are often used in economics areas such as utility function , forecasting, cost-befit analysis, etc.

It is necessary to construct the scatter-diagram for the data before a quadratic regression can be constructed from the graph created.

The goal of regression analysis is to model the expected value of a dependent variable y in terms of the value of an independent variable (or vector of independent variables) x. In simple linear regression, the model

$y = a_0 + a_1 x + \varepsilon, \,$

is used, where ε is an unobserved random error with mean zero conditioned on a scalar variable x. In this model, for each unit increase in the value of x, the conditional expectation of y increases by a₁ units.
In many settings, such a linear relationship may not hold. For example, if we are modeling the yield of a chemical synthesis in terms of the temperature at which the synthesis takes place, we may find that the yield improves by increasing amounts for each unit increase in temperature. In this case, we might propose a quadratic model of the form

$y = a_0 + a_1x + a_2x^2 + \varepsilon. \,$

In this model, when the temperature is increased from x to x + 1 units, the expected yield changes by a₁ + a₂ + 2a₂x. The fact that the change in yield depends on x is what makes the relationship nonlinear (this must not be confused with saying that this is nonlinear regression; on the contrary, this is still a case of linear regression).