## BCG Matrix

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In statistics and econometricsparticularly in regression analysisa dummy variable also known as an indicator variabledesign variableBoolean indicatorbinary variableor qualitative variable [1] [2] is one that takes the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.

A dummy variable can thus be thought of as a truth value represented as a numerical value 0 or 1 as is sometimes done in computer programming.

Dummy variables are "proxy" variables or numeric stand-ins for qualitative facts in a regression model. In regression analysis, the dependent variables may be influenced not only by quantitative variables income, output, prices, etc. A dummy independent variable also called a dummy explanatory variable which for some observation has a value of 0 will cause that variable's coefficient to have no role in influencing the dependent variablewhile when the dummy takes on a value 1 its coefficient acts to alter the intercept.

For example, suppose membership in a group is one of the qualitative variables relevant to a regression. If group membership is arbitrarily assigned the value of 1, then all others would get the value 0. Then the intercept the value of the dependent variable if all other explanatory variables hypothetically took on the value zero would be the constant term for non-members but would be the constant term plus the coefficient of the membership dummy in the case of group members.

Dummy variables are used frequently in time series analysis with regime switching, seasonal analysis and qualitative data applications. Dummy variables are involved in studies for economic forecastingbio-medical studies, credit scoringresponse modelling, etc. Dummy variables may be incorporated in traditional regression methods or newly developed modeling paradigms.

Dummy variables are incorporated in the same way as quantitative variables are included as explanatory variables in regression product name binary matrix proxy. For example, if we consider a Mincer-type regression model of wage determination, wherein wages are dependent on gender qualitative and years of education quantitative:. Note that the coefficients attached to the dummy variables are called differential intercept coefficients.

The model can be depicted graphically as an intercept shift between females and males. Dummy variables may be extended to more complex cases. For example, seasonal effects may be captured by creating dummy variables for each of the seasons: In the panel dataproduct name binary matrix proxy effects estimator dummies are created for each of the product name binary matrix proxy in cross-sectional data e.

However in such regressions either the constant term has to be removed or one of the dummies has to be removed, with its associated category becoming the base category against which the others are assessed in order to avoid the dummy variable trap:. The constant term in all regression equations is a coefficient multiplied by a regressor equal to one. When the regression is expressed as a matrix equation, the matrix of regressors then consists of a column of ones the constant termvectors of zeros and ones the dummiesand possibly other regressors.

If one includes both male and female dummies, say, the sum of these vectors is a vector of ones, since every observation is categorized as either male or female. This sum is thus equal to the constant term's regressor, the first vector of ones. As result, the regression equation will be unsolvable, even by product name binary matrix proxy typical pseudoinverse method.

This is referred to as the dummy variable trap. The trap can be avoided by removing either the constant term or one of the offending dummies. The removed dummy then becomes the base category against which the other categories are compared. A regression model in which the dependent variable is quantitative in nature but all the explanatory variables are dummies qualitative in nature is called an Analysis of Variance ANOVA model.

Suppose we want to run a regression to find out if the average annual salary of public school teachers differs among three geographical regions in Country A with 51 states: Say that the simple arithmetic average salaries are as follows: The arithmetic averages are different, but are they statistically different from product name binary matrix proxy other? To compare the mean values, Analysis of Variance techniques can be used. The regression model can be defined as:.

In this model, we have only qualitative regressors, taking the value of 1 if the observation belongs to a specific category and 0 if it belongs to any other category. Now, taking the expectation of both sides, we obtain the following:. The error term does not get included in the expectation values as it is assumed that it satisfies the usual OLS conditions, i. The expected values product name binary matrix proxy be interpreted as follows: Thus, the mean salaries of teachers in the North and South is compared against the mean salary of the teachers in the West.

Hence, the West Region becomes the base group or the benchmark group ,i. The omitted categoryi. The regression result can be interpreted as: To find out if the mean salaries of the teachers in the North and South are statistically different from that of the teachers in the West the comparison categorywe have to find out if the slope coefficients of the regression result are statistically significant.

For this, we need to consider the p values. The model is diagrammatically shown in Figure 2. Here, Marital Status and Geographical Region are the two explanatory dummy variables.

In this model, a single dummy is assigned to each qualitative variable, one less than the number of categories included in each. Here, the base group product name binary matrix proxy the omitted product name binary matrix proxy Unmarried, Non-North region Unmarried people who do not live in the Product name binary matrix proxy region.

All comparisons would be made in relation to this base group or omitted category. Thus, if more than one qualitative variable is included in the regression, it is important to note that the omitted category should be chosen as the benchmark category and all comparisons will be made in relation to that category.

The intercept term will show the expectation of the benchmark category and the slope coefficients will show by how much the other categories differ from the benchmark omitted category. They statistically control for the effects of quantitative explanatory variables also called covariates or control variables.

If we include a quantitative variable, State Government expenditure on public schools per pupilin this regression, we get the following model:. Figure 3 depicts this model diagrammatically. The average salary lines are parallel to each other by the assumption of the model that the coefficient of expenditure product name binary matrix proxy not vary by state. The trade off shown separately in the graph for each category is between product name binary matrix proxy two quantitative variables: Quantitative regressors in regression models often have an interaction among each other.

In the same way, qualitative regressors, or dummies, can also have interaction effects between each other, and these interactions can be depicted in the regression model. For example, in a regression involving product name binary matrix proxy of wages, if two qualitative variables are considered, namely, gender and marital status, there could be an interaction between marital status and gender. With the two qualitative variables being gender and marital status and with the quantitative explanator being years of education, a regression that is purely linear in the explanators would be.

This specification does product name binary matrix proxy allow for the possibility that there may be an interaction that occurs between the two qualitative variables, D 2 and D 3. For example, a female who is married may earn wages that differ from those of an unmarried male by an amount that is not the same as the sum of the differentials for solely being female and solely being married.

Then the effect of the interacting dummies on the mean of Y is not simply additive as in the case of the above specification, but multiplicative also, and the determination of wages can be specified as:. Thus, an interaction dummy product of two dummies can alter the dependent variable from the value that it gets when the two dummies are considered individually. However, the use of products of dummy variables to capture interactions can be avoided by using a different scheme for categorizing the dataâ€”one that specifies categories in terms of combinations of characteristics.

This specification involves the same number of right-side variables as does the previous specification with an interaction term, and the regression results for the predicted value of the dependent variable contingent on X ifor any combination of qualitative traits, are identical between this specification and the interaction specification. A model with a dummy dependent variable also known as a qualitative dependent variable is one in which the dependent variable, as influenced by the explanatory variables, is qualitative in nature.

Some decisions regarding 'how much' of an act must be performed involve a prior decision making on whether to perform the act or not. For example, the amount of output to produce, the cost to be incurred, etc. Such "prior decisions" become product name binary matrix proxy dummies in the regression model. For example, the decision of a worker to be a part of the labour force becomes a dummy dependent variable.

The decision is dichotomousi. So the dependent dummy variable Participation product name binary matrix proxy take on the value 1 if participating, 0 if not participating. Affiliation to a Political Party. When the qualitative dependent dummy variable has more than two values such as affiliation to many political partiesit becomes a multiresponse or a multinomial or polychotomous model. Analysis of dependent dummy variable models can be done through different methods.

One such method is the usual OLS method, which in this context is called the linear probability model. Product name binary matrix proxy is the underlying concept of the logit and probit models. These models are discussed in brief below. An ordinary least squares model in which the dependent variable Y is a dichotomous dummy, taking the values of 0 and 1, is the linear probability model LPM.

The model is called the linear probability model because, the regression is linear. Thus the relationship between the independent and dependent variables is necessarily non-linear. For this purpose, a cumulative distribution function CDF can be used to estimate the dependent dummy variable regression. Figure 4 shows an 'S'-shaped curve, which resembles the CDF of a random variable. In this model, the probability is between 0 and 1 and the non-linearity has been captured. The choice of the CDF to be used is now the question.

Two alternative CDFs can be used: The shortcomings of the LPM led to the development of a more refined product name binary matrix proxy improved model called the product name binary matrix proxy model.

In the logit model, the cumulative distribution of the error product name binary matrix proxy in the regression equation is logistic. The logit model is estimated using the maximum likelihood approach. The model is then expressed in the form of the odds ratio: Taking the natural log of the odds, the logit L i is expressed as.

This relationship shows that L i is linear in relation to X ibut the probabilities are not linear in terms of X i. Another model that was developed to offset the disadvantages of the LPM is the probit model. The probit model uses the same approach to non-linearity as does the logit model; however, it uses the normal CDF instead of the logistic CDF.

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TFS can be installed on a Windows server or client operating system. For earlier versions of TFS, you can use either the bit or bit operating systems when a bit version is available. Windows Server, version is not supported. While TFS supports installation on client OSes, we don't recommend this except for evaluation purposes or personal use. The proxy feature is available only if you installed Team Foundation Server on a server operating system.

Review these hardware recommendations to determine the optimal hardware to use for Team Foundation Server Proxy. Unlike operating system requirements, hardware recommendations for proxy are different than those for setting up the application tier of Team Foundation Server. The application tier of TFS requires more robust hardware than the proxy feature does. These recommendations are guidelines for Team Foundation Server Proxy. Recommended hardware is based on the size of the team that will use the proxy server.

Usually this is the team in your remote office. The larger the team, the more robust your hardware must be. Microsoft supports the virtualization of Team Foundation Server in supported virtualization environments. For more information, see the following pages on the Microsoft website:.

SQL Server has increased hardware requirements compared with previous versions. Certain configurations might hurt TFS performance. For more information, read TFS Update 2: This isn't a requirement because the bug only affects a small number of instances, but we wanted you to be aware of it.

Your limits on database read operations Microsoft does not support any read operations against the TFS databases that originate from queries, scripts,. If Microsoft Support determines that those read operations prevent them from solving your problem, the entire database will be unsupported. To return the database to a supported state, all unsupported read operations must stop.

For more information, see: The Express edition is only recommended for evaluation purposes, personal use, or for very small teams. We recommend Standard or Enterprise for all other scenarios. For more information, see Discontinue SharePoint integration: TFS and earlier versions. NTLM is the recommended authentication provider. In SharePoint Server , Microsoft deprecated Windows classic-authentication in favor of claims-based authentication. If you plan to install SharePoint, make sure that the version of SharePoint you want to use is compatible with the server operating system you're using.

You can use SharePoint Server. If you use the enterprise version of SharePoint Server, you must configure it for dashboard compatibility. Team Foundation Server contains dashboards that use SharePoint Products features to display team data. The dashboards that are available to you depend on the version of SharePoint Products that you use.

If you use any supported enterprise edition of SharePoint Server, you get five dashboards that are based on Microsoft Excel. You can install Team Foundation Server on more than one server if they are all joined to an Active Directory domain that is based on a functional level that TFS supports. You can install TFS on a single server that is joined to an Active Directory domain or that is a member of a workgroup.

If you use reporting, you also need a report reader account when you install Team Foundation Server. This topic describes the requirements for service accounts and the report reader account for installation.

Team Foundation Server requires multiple identities for installation, but you can use a single account for all the identities, as long as that account meets the requirements for all the identities for which you use it. New for this release is a tutorial available for Team Foundation Server installation that covers how to create accounts and groups for a single server installation. For more information, see Set up groups for use in TFS deployments.

If you use domain accounts for your service accounts, you should use a different identity for the report reader account. The report reader account is the identity that is used to gather information for reports.

If you use reporting, you must specify a report reader account when you install Team Foundation Server. If you install Team Foundation Server with the default options, the report reader account is also used as the identity of the service account for SharePoint Foundation.

These service accounts become the identity for the installed component. By default, every component uses a built-in account such as Network Service as its service account. You can change this account to a user account when you install the component, but you must ensure that any user accounts that you use have the Log on as a service permission.

Built-in accounts do not use passwords and already have the Log on as a service permission, making them easier to manage, especially in a domain environment. The service accounts in the following table are the identities for Team Foundation Server and its components. The service accounts in the following table are the identities for Release Management Server and the Microsoft Deployment agent.

For a step-by-step procedure, go here: The service account for SharePoint Products is also the identity of the application pool for the SharePoint Central Administration site.

You do not have to use these placeholder names for any accounts that you might create. Team Foundation Server doesn't require Project Server, but if you use Project Server, you must use a supported version. If you run multiple servers with Project Server in a web farm, you must install these extensions on every application-tier and web-tier server in that farm.

NTLM is the recommended authentication. For more information, see this topic: Project Server is an extension of SharePoint Products. Team Foundation Server recommends you use a web application running on port 80 for integration with SharePoint Products and you can use this same web application to host the Project Server projects.

You can also run Project Server on its own SharePoint farm, separate from any farm where you might host team project portal sites. Team Foundation Server has no topology requirements for Project Server.

For performance reasons, we recommend you run Project Server on a server other than Team Foundation Server. If you want to set up a sandbox integration of Project Server and Team Foundation Server, you could install all the products on a single server for demonstrations or test purposes.

We don't always immediately support major new versions of our dependencies like SQL Server because we sometimes have to do updates to add support for those versions. However, once we support a major version, we always support the latest service pack immediately when it releases.

We work with those teams to test the service pack before release. Team Foundation Server can scale from an Express installation on a laptop used by a single person all the way up to a highly available deployment used by thousands of people and comprising multiple application tiers behind a load balancer, multiple SQL instances using SQL Always On, etc.

The following recommendations should apply to most TFS deployments, but your requirements may vary depending on the usage of your team. For example, if you have particularly large Git repositories or Team Foundation Version Control branches, you may need higher spec machines that what are listed below.

Note that all of the machines discussed below could be either physical or virtual. This configuration should support up to users of core source control TF VC or Git and work item tracking functionality. Extensive use of automated build, test, or release would likely cause performance issues. Use of search or reporting features would not be recommended with this configuration.

For example, increasing RAM to 8 GB should enable a single server deployment to scale up to users. For evaluation or personal use, you can use a a basic configuration with as little as 1 GB of RAM, but clearly this would not be recommended for a production server used by more than one person. Scaling beyond users; enabling extensive use of automated build, test, or release; enabling use of Code Search; enabling use of reporting features; or enabling SharePoint integration typically requires expanding to a multiple server deployment.

If you plan to extensively use build, test, or release automation, we recommend using higher spec application and data tiers to avoid performance issues. For example, a team of might use a multiple server deployment that is more in line with the recommendations for a team of , users. We also recommend that you keep an eye on your automated processes to ensure that they are efficient - for example, retrieve data from source control incrementally during builds whenever possible, rather than fully refreshing on each build.

If you plan to use Code Search, we typically recommend setting up a separate server for it. For more details, see hardware requirements for Code Search. If you plan to use reporting features, we recommend setting up a separate server for your warehouse database and Analysis Services cube or using a higher spec data tier.

If you plan to use SharePoint integration, we recommend setting up a separate server for your SharePoint instance or using a higher spec application tier. If you want to guarantee high availability, you should consider multiple application tiers behind a load balancer and multiple SQL instances with your TFS DBs in an Always On availability group.

It normally makes sense to run the build service on a machine separate from the TFS application tier. Hardware requirements for the build service are the same as the operating system on which it is running.

However, you can optimize build service performance by tailoring the hardware specs of your build machine to the types of builds your team will use. If you install SharePoint Products, you will need more robust hardware than what is listed in the previous table.

You can install TFS in various languages on supported operating systems in various languages. However, you cannot use every combination of localized operating system with TFS and you can't install multiple languages on a single TFS server. The language of the installation of SharePoint Products can also complicate your deployment.

However, you can add an appropriate language pack to the server that is running SharePoint Products to meet requirements for Team Foundation Server. The following rules clarify the language requirements for installations of Team Foundation Server. If you are running an English language operating system, you can install any language version of Team Foundation Server.

If you are not running an English language operating system, you must install the English version of Team Foundation Server or the version of Team Foundation Server that has been localized for the same language as the operating system. If you want to use SharePoint Products, it must match the language of the installation of Team Foundation Server, or you must install the language pack that matches the language of your installation of Team Foundation Server.

For example, you can install a Japanese version of Team Foundation Server on an English or Japanese operating system but not on a German operating system. The following components do not have additional language requirements that are specific to working with Team Foundation Server:.