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ST2218 Advanced Statistical Methods for Business Assignment Sample NUI Galway Ireland

ST2218 Advanced Statistical Methods for Business is a graduate-level course that covers a variety of advanced statistical topics with an emphasis on their applications in business.

The course begins with an overview of advanced statistical methods, including predictive modelling and time series analysis. This is followed by a detailed study of hypothesis testing, including both Neyman-Pearson and Bayesian approaches. The course then turns to more specific topics such as regression analysis, forecasting, and data mining. Throughout the course, students will learn how to apply these techniques to real-world business problems. 

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In this section, we are describing some assigned briefs. These are:

Assignment Brief 1: Describe the conditions when a parametric test or a non-parametric test alternative is more suitable in certain problems and complete non-parametric testing procedures: the Sign Test, the Wilcoxon Rank Sum Test, the Wilcoxon Signed Rank Test.

In general, parametric tests are more powerful than non-parametric tests, but there are some situations where a non-parametric test is more appropriate. Situations when a parametric test might not be appropriate include when the data are not normally distributed or when there is significant multicollinearity in the predictors. In addition, parametric tests generally require larger sample sizes than non-parametric tests to produce reliable results.

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There are also some situations where a complete non-parametric testing procedure may be more suitable. This situation typically arises when the assumptions underlying the parametric tests are severely violated. In these cases, the use of a non-parametric test can help to increase the robustness of the results.

The following sections describe the conditions under which each of the three non-parametric tests would be more appropriate than a parametric alternative.

1) The Sign Test:

The Sign Test is used when two groups are expected to be different, but the direction of the difference is not known. This test is appropriate when the data are not normally distributed and when there is no significant multicollinearity.

2) The Wilcoxon Rank Sum Test:

The Wilcoxon Rank Sum Test is used when two groups are expected to be different, and the direction of the difference is known. This test is appropriate when the data are not normally distributed and when there is no significant multicollinearity.

3) The Wilcoxon Signed Rank Test:

The Wilcoxon Signed Rank Test is used when two groups are expected to be different, but the direction of the difference is not known. This test is appropriate when the data are not normally distributed and when there is significant multicollinearity.

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Assignment Brief 2: Complete advanced analysis of simple linear regression models, including analysis of variance (ANOVA) in the response variable, calculation of R-squared and completion of the ANOVA table, further exploration into inference for regression model parameters, including individual t-tests for model parameters and the F-test through calculation of ANOVA table, check assumptions, diagnostic and model checking, apply transformations, using the model for prediction, prediction intervals, and confidence intervals.

Simple linear regression is a powerful tool that can be used to predict response variables. However, in order t perform a complete analysis of a simple linear regression model, including ANOVA and calculation of R-squared, it is necessary to understand the underlying assumptions of the model. In this article, we will go over these assumptions and discuss how they impact the model results. 

One of the key assumptions of simple linear regression is that there is a linear relationship between the predictor variable(s) and the response variable. That is, we are assuming that the change in the response variable is directly proportional to the change in the predictor variable (or variables). If this assumption does not hold, then our analysis may be inaccurate.

Another important assumption is that the error term is normally distributed. This means that the variance of the error term is constant and that the error terms are independent of each other. Violation of this assumption can lead to inaccurate results.

It is also important to check for multicollinearity in the data. This is when there are two or more predictor variables that are highly correlated with each other. This can impact the results of the regression model and should be avoided if possible.

Once the assumptions have been checked, we can proceed with the analysis. We will first calculate the ANOVA table to see if there is a significant difference between the groups. Next, we will calculate R-squared to see how well the model predicts the response variable. Finally, we will conduct a t-test for each of the model parameters to see if they are significantly different from zero.

After performing the analysis, we can conclude that there is a significant difference between the groups and that the model predicts the response variable well. We can also see that the individual t-tests for the model parameters are all significant, meaning that each of the predictor variables has a significant impact on the response variable.

Now that we have completed the analysis, we can use the model to make predictions. We can do this by using the fitted values from the model and plugging them into the equation for the response variable. We can also create prediction intervals and confidence intervals to give us a range of values that we expect the response variable to fall within.

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Assignment Brief 3: Carry out analysis for problems requiring a multiple regression model, i.e. many candidate predictors may be used to explain the variability in the response variable. This includes interpretation of regression coefficients, constructing confidence intervals, and carrying out hypothesis tests for regression parameters through individual t-tests and the ANOVA F-test, using the model for prediction, prediction intervals, and confidence intervals, model-building, variable selection procedures, and adjusted R-squared.

In a multiple regression model, many candidate predictors may be used to explain the variability in the response variable. The goal is to identify the predictor(s) that best explain the variability in the response variable. This can be done through various model selection techniques. For example, you could use forward selection, backward selection, or stepwise selection. Once the best model has been identified, you can then interpret the coefficients of the predictor variables to understand how they affect the response variable.

It is also important to assess the goodness of fit of the model. This can be done by calculating R-squared and adjusted R-squared. R-squared measures the percent of the variability in the response variable that is explained by the predictor variables, while adjusted R-squared adjusts for the number of predictor variables in the model.

Another important consideration is the assumption of normality. This assumption must be met for the results of the regression analysis to be valid. Violation of this assumption can lead to inaccurate results.

It is also important to check for multicollinearity in the data. This is when there are two or more predictor variables that are highly correlated with each other. This can impact the results of the regression model and should be avoided if possible.

Assignment Brief 4: Extend knowledge of multiple regression to the interpretation of model coefficients for models with qualitative/categorical predictors and analysis of covariance, ANCOVA.

In multiple regression, the model coefficients are used to estimate the average change in the dependent variable (Y) associated with a unit change in each independent variable (X).

However, when a predictor is categorical (e.g., sex), its coefficient doesn’t estimate the average change in Y associated with a unit change in X. Rather, it estimates the difference in Y between two categories of the predictor (e.g., men and women). This difference is called a “betweens group” or “between category” effect.

The analysis of covariance (ANCOVA) is used to determine whether there is a statistically significant difference in Y between two or more groups, after controlling for the effects of other variables (covariates).

ANCOVA is similar to multiple regression in that it estimates the effect of each independent variable on the dependent variable. However, ANCOVA also includes a term for the interaction between the independent variables and the dependent variable. This interaction term represents the combined effect of the independent variables on the dependent variable.

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Assignment brief 5: Complete basic time series analysis, including descriptive analysis via calculation of various index numbers, recognize time series components, apply smoothing models such as Moving-average models, Exponential Smoothing, and Holt-Winters Smoothing, and apply seasonal regression models using additive models with indicator variables, describe autocorrelation and carry out the Durbin-Watson test, use models to forecasting trends and seasonality, measure Forecasting accuracy using MAD, MAPE, and RMSE.

Time series analysis is a type of statistical technique that is used to examine data points that are connected in time. This means that time series analysis can be used to identify patterns, trends, and correlations in data. Time series analysis can also be used to forecast future data points based on past behaviour.

Many different techniques can be used for time series analysis. Some of the most common include:

Calculating various index numbers: Many time series have index numbers associated with them. These index numbers can provide information about overall trends in the data. Commonly used index numbers include the Consumer Price Index (CPI) and the Gross Domestic Product (GDP) deflator.

Recognizing time series components: Time series data can be decomposed into its constituent parts, which can help to identify patterns and trends. The three main components of a time series are the trend, the seasonality, and the noise.

Applying smoothing models: Smoothing models are used to remove noise from data points. This can make it easier to identify patterns and trends. Commonly used smoothing models include moving-average models, exponential smoothing, and Holt-Winters smoothing.

Applying seasonal regression models: Seasonal regression models are used to predict future data points based on past behaviour. These models take into account the fact that many time series have seasonality, which means that they tend to follow a repeating pattern over time. Seasonal regression models can be used to forecast future data points based on this past behaviour.

Describing autocorrelation: Autocorrelation is the degree to which data points are correlated with each other over time. This can be used to identify patterns in time series data.

Carrying out the Durbin-Watson test: The Durbin-Watson test is used to test for autocorrelation in time series data. This test can be used to identify patterns in time series data.

Measuring forecasting accuracy: There are many ways to measure the accuracy of a forecast. Some of the most common include the mean absolute error (MAE), the mean absolute percentage error (MAPE), and the root means squared error (RMSE).

Time series analysis is a type of statistical technique that is used to examine data points that are connected in time. This means that time series analysis can be used to identify patterns, trends, and correlations in data. Time series analysis can also be used to forecast future data points based on past behaviour.

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Assignment brief 6: Apply methods in Quality Control including compilation and interpretation of statistical control charts for monitoring the mean of a process, monitoring the variation of a process, and for monitoring the proportion of defectives generated by a process, diagnosing the cause of variation, and capability analysis.

There are a variety of methods that can be used in quality control, including the compilation and interpretation of statistical control charts for monitoring the mean of a process, monitoring the variability of a process, and detecting special causes. By using these methods, businesses and organizations can ensure that their products or services meet the required standards for quality.

Statistical control charts are a type of quality control chart that is used to monitor processes. These charts can be used to monitor the mean of a process, the variability of a process, and the proportion of defectives in a process. Control charts help businesses and organizations to detect special causes of variation so that they can be addressed.

Capability analysis is another method that can be used in quality control. This method is used to assess whether a process is capable of meeting the required specifications for a product or service. Capability analysis can be used to determine if a process is capable of producing products or services that meet the desired quality standards.

Assignment brief 7: To communicate the results of analyses in clear, structured reports.

There are many ways to communicate the results of your data analysis, but one of the most effective is to create a clear and concise report. This ensures that your audience understands your findings and can take action on them.

To start, consider what information you want to include in your report. Make sure that it is pertinent to your audience and supports your overall objective. Then, organize your thoughts and present them in a logical order. Use headings and subheadings to break up large chunks of text and make it easy to scan. And finally, use simple language that can be understood by everyone.

While graphs and charts can help illustrate your data, be careful not to overload your reports with too many visuals. A few well-placed graphs or charts can be more effective than a page full of them.

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