A Thesis Submitted for a PhD degree at ASU

A thesis submitted for the degree of Doctor of Philosophy at Arizona State University in 2023. Ira A. Fulton Schools of Engineering

1 Introduction

This is where you introduce the main ideas of your thesis, and an overview of the context and background.

In a PhD, Chapter 2 would normally contain a literature review. Typically, Chapters 3–5 would contain your own contributions. Think of each of these as potential papers to be submitted to journals. Finally, Chapter 6 provides some concluding remarks, discussion, ideas for future research, and so on. Appendixes can contain additional material that don’t fit into any chapters, but that you want to put on record. For example, additional tables, output, etc.

1.1 Quarto

In this template, the rest of the chapter shows how to use quarto. The big advantage of using quarto is that it allows you to include your R or Python code directly into your thesis, to ensure there are no errors in copying and pasting, and that everything is reproducible. It also helps you stay better organized.

For details on using Quarto, see http://quarto.org.

1.2 Data

Included in this template is a file called sales.csv. This contains quarterly data on Sales and Advertising budget for a small company over the period 1981–2005. It also contains the GDP (gross domestic product) over the same period. All series have been adjusted for inflation. We can load in this data set using the following code:

Any data you use in your thesis can go into the data directory. The data should be in exactly the format you obtained it. Do no editing or manipulation of the data prior to including it in the data directory. Any data munging should be scripted and form part of your thesis files (possibly hidden in the output).

1.3 Figures

Figure 1.1 shows time plots of the data we just loaded. Notice how figure captions and references work. Chunk names can be used as figure labels with fig- prefixed. Never manually type figure numbers, as they can change when you add or delete figures. This way, the figure numbering is always correct.

Figure 1.1: Quarterly sales, advertising and GDP data.

1.4 Results from analyses

We can fit a dynamic regression model to the sales data.

Series: Sales 
Model: LM w/ ARIMA(1,0,0)(0,1,1)[4] errors 

Coefficients:
         ar1     sma1     GDP  AdBudget
      0.2189  -0.9016  0.9742    2.2824
s.e.  0.1022   0.0715  0.4387    0.3930

sigma^2 estimated as 1677:  log likelihood=-493.94
AIC=997.87   AICc=998.54   BIC=1010.69

If \(y_t\) denotes the sales in quarter \(t\), \(x_t\) denotes the corresponding advertising budget and \(z_t\) denotes the GDP, then the resulting model is: \[ y_t - y_{t-4} = \beta (x_t-x_{t-4}) + \gamma (z_t-z_{t-4}) + \phi_1 (y_{t-1} - y_{t-5}) + \Theta_1 \varepsilon_{t-4} + \varepsilon_t \tag{1.1}\] where \(\beta = 2.28\), \(\gamma = 0.97\), \(\phi_1 = 0.22\), and \(\Theta_1 = -0.90\). We can reference this equation using Equation 1.1.

1.5 Tables

Let’s assume future advertising spend and GDP are at the current levels. Then forecasts for the next year are given in Table 1.1.

Table 1.1: Forecasts for the next year assuming Advertising budget and GDP are unchanged.

Quarter	Sales forecast
2006 Q1	1000.2
2006 Q2	1013.1
2006 Q3	1076.7
2006 Q4	1003.5

Again, notice the use of labels and references to automatically generate table numbers.