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# ST312 Applied Statistics II Assignment Sample NUI Galway Ireland

ST312 Applied Statistics II is a follow-up course to ST311 Applied Statistics I. In this course, students will learn advanced statistical methods and their applications. The course will cover topics such as advanced regression analysis, multivariate analysis, time series analysis, and experimental design. Through lectures and exercises, students will learn how to apply these methods to real-world data sets. By the end of the course, students should be able to communicate their results and findings from statistical analyses.

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

### Assignment Task 1: Discuss topics in experiment design and carry out analysis for data collected from a completely randomized design, a randomized block design, and two-factor studies with interaction effects, and interpret the results concerning the data application.

Designing experiments can be a complex task, and there are a variety of different approaches that can be taken. One common approach is to use a completely randomized design, in which each unit (e.g., individual, the plot of land, etc.) is assigned to treatment at random. This type of design is easy to implement and provides good information about the main effects (i.e., the effect of each treatment on the overall response variable).

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However, completely randomized designs can suffer from problems with reduced precision due to confounding factors (i.e., variables that are not controlled for in the experiment but could influence results). To address this issue, other types of designs can be used, such as randomized block designs or two-factor studies with interaction effects.

In a randomized block design, units are first grouped into blocks (e.g., based on similar characteristics) and then randomly assigned to treatments within each block. This approach can help to control for confounding factors and increase precision by reducing variability between units within blocks.

Two-factor studies with interaction effects involve assigning two or more treatments to units and then observing the response. This type of design can be used to study the effect of interactions between treatments on the response variable.

### Assignment Task 2: Formulate a logistic regression model and generalized linear model for a qualitative response, calculate and interpret estimated coefficients and make statistical inferences on the fitted model by carrying out statistical tests using parameter estimates, obtain fitted values and predictions at new data points, together with associated prediction and confidence intervals.

To formulate a logistic regression model, we’ll need to start with a binary response variable. This can be something like pass/fail, SUV/not SUV, M/F, etc. We’ll also need a set of predictor variables that we think might be related to the response variable.

For simplicity, let’s assume that our response variable is whether or not an individual purchase an SUV and our predictors are income, age, and gender. We can then write our logistic regression model as follows:

logit(p)=β0+β1×Income+β2×Age+β3×Female

where p is the probability of purchasing an SUV. The terms β0, β1, β2, and β3 are the regression coefficients that we need to estimate.

To estimate the regression coefficients, we’ll need a dataset that includes observations on income, age, gender, and whether or not an individual purchased an SUV. We can then use maximum likelihood estimation to fit the model to the data and obtain estimates for the regression coefficients.

Once we have the estimated coefficients, we can use them to make predictions about whether or not an individual is likely to purchase an SUV. For example, let’s say we have a dataset that includes observations on income, age, and gender but not whether or not an individual purchased an SUV. We can then use our fitted logistic regression model to make predictions for each individual in the dataset.

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### Assignment task 3: Apply various techniques in the analysis of a multivariate response, including topics from, principal components analysis, cluster analysis, and time series analysis.

Multivariate response data can be analyzed in a variety of ways, including principal components analysis (PCA), cluster analysis, and time series analysis.

PCA is a technique that can be used to reduce the dimensionality of data by transforming a set of correlated variables into a smaller number of uncorrelated variables. This transformation is often called “eigenvectors” and “eigenvalues” and can be used to simplify data so that it is more easily understood and interpreted.

Cluster analysis is a technique that can be used to group observations together in such a way that members of the same group are more similar to each other than they are to members of other groups. This technique can be useful for identifying natural clusters in data, such as groups of customers with similar purchasing habits.

Time series analysis is a technique that can be used to analyze data that have been collected over time. This type of analysis can be used to identify trends and patterns in data, and to make predictions about future values.

### Assignment Task 4: Carry out analysis and testing procedures discussed with the use of software, R.

Several software programs can be used for data analysis and statistical testing. One such program is R, which is a free, open-source software package. R can be used for a variety of data analysis tasks, including the creation of graphs and charts, the calculation of statistics, and the testing of hypotheses.

R is a powerful program that can be used by researchers to carry out complex data analysis tasks. However, it is also fairly complex to use and requires some knowledge of programming to be able to use it effectively. For this reason, R may not be suitable for everyone and may be more suited to more experienced users.

### Assignment Task 5: Compile a statistical report, i.e. prepare a typed document that introduces the statistical research question being explored, describes the data collection method applicable to the research, describes relevant features of the sample data obtained, and outlines conclusions from the inferential statistical analysis carried out using the sample data, incorporating output and plots from statistical software.

The purpose of this report is to explore the relationship between age and income. The data for this report was collected from a survey of 100 individuals.

The results of the survey showed that there was a positive correlation between age and income. This means that as age increases, so does income. However, the correlation was not statistically significant, meaning that the difference in income between different age groups may be due to chance alone.

There are several possible explanations for this result. One possibility is that the sample size was too small to detect a significant difference. Another possibility is that there may be other factors that affect income, such as education level or occupation, that were not accounted for in this study.

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