Generating a Unique Population - Assignment Example

Example: The first two letters of my first name are R and A which are the 18th and the 1st letter of the English alphabet, respectively. The first two letters of my surname are M and U which are the 13th  and the 21st  letter of the English alphabet, respectively. So I shall generate R = 853 ( = 800 + 18 + 1 + 13 + 21) random numbers to form my ‘population’.

Distribution binomial.
p-value (choose any number p such that 0 <p < 1
Several trials n where n is an integer satisfying 10 ≤ n ≤ 20. 

Consider two estimators of the population mean (m),    ≡ and  ≡ (X1 +X2)/2. That is, the sample mean and the average of only the first two observations of a randomly drawn sample X.

Take 30 samples (each of size 30) from the population.
Present the distributions of each of and  (Give a screenshot of the values of and you have obtained in your Word document). (10 marks)
Calculate the bias and standard error of the two estimators. Show all workings and write down any formula you may have used to do the calculations. (20 marks)

Use the file “statistics assignment”. Choose Internet users (per 100 people) (IN) as the dependent variable. Select 3 independent variables from:
- Urban population (U),
- Literacy Rate (L),
- GDP (G),
- GNI per capita (GN).

Manually (but randomly) select n (20 ≤ n ≤ 25) countries (do not use any random selection mechanism) to construct the data set. Enter the observations on each of the four variables corresponding to each country you have selected into a Stata data file and save this file. Your Stata data editor should now show a data matrix with dimensions (n X 4) where the value of n is chosen by you as per the requirement.

Select any one independent variable from the three in your dataset and denote it by X. Denote the dependent variable IN by Y. Use a calculator/software and your sample to calculating ∑X, ∑Y, ∑XY, and ∑X2. Use these values to write down the pair of ‘normal equations’ the solutions of which give the constant term and the slope of the Ordinary Least Squares (15 marks)

Write down the equivalent matrix representation of the normal equations you have written in part (i) above. Use Stata to solve these equations using matrices. (20 marks)

Use a calculator/software and the values of ∑X, ∑Y, ∑XY, and ∑X2 to show that the second-order conditions for a unique minimum are satisfied for the solution you have obtained. (5 marks)

Construct the multiple regression model by denoting the dependent and the selected independent variables using the Roman characters Y, X2, X3, and X4, respectively. For example, if you choose an Urban population, Literacy Rate, and GDP then you should define the model as Y = b1 + b2X2 +b3X3 + b4X4  + ɛ where Y ≡ Internet users; X2 ≡  Urban population; X3≡  Literacy Rate and X4 ≡  GDP.

Run a Stata regression of the dependent variable Y values on the three explanatory variables you have chosen and a constant. Use the regression output to explain why and how the F-statistic was calculated by the software and how it can be used to test for the overall relevance of the regression model. (30 marks)

All Excel, Stata, and Word files are to be submitted. You cannot be given any credit if any of the electronic files are not submitted.
Recording your work in a Stata log file is optional. However, you must submit such a file should you create one.
Write all your answers using a text editor such as Microsoft Word. Copy and paste any relevant data analysis as pictures in this text document.
Remember, it is the text document that will be read and marked; the data files (Excel and Stata) are for verification purposes only. So make sure you present your answers well.
Do not write anything unrelated to the numeric analysis you have performed.
Stay within the specified word limit.