Accounting

1. There are three tasks in this coursework. 


2. Each task asks you to perform some statistical computing. These will be based on the dataset and samples you generate (see instructions below) using Excel as well as statistical analyses using the software Stata. 


3. You need to work independently and generate your unique dataset by the methods shown below. Please note that failure to follow this step will be considered as Academic Misconduct 


4. You need to perform the calculations, show all workings, type up and save your work in a single Microsoft Word document and submit it via Moodle before the deadline set. 


5. Corresponding to each question within a task, there will be one numeric answer based upon the calculations you have performed above. You will need to enter this answer in an Excel spreadsheet as specified below. Save the Excel file when you have entered all the answers as per instructions and submit it via Moodle before the deadline. 


6. NOTE THAT IT IS THE ANSWERS GIVEN IN THE EXCEL FILE THAT WILL BE MARKED AND YOU WILL RECEIVE THE COURSEWORK GRADE BASED ON THESE MARKS. 


7. The submitted Word file is for verification purposes only. This means that the examiner must be able to verify how and where you got your numeric answers from. Therefore, you cannot be given any marks if the workings and calculations are not shown in the Word document you submit. 


8. You need to run the regression analysis using Stata and Stata only. You will not be given any credit if you use any other software to run the regression. You must create and submit a Stata .log file detailing all the computations you perform using Stata.

Task 1 (38 marks)

Task 1 is an exercise on properties of two estimators, 1 and 2 of the population mean 
Note: Task 1 must be performed using Microsoft Excel.

Open the Excel document Coursework Data and click open the ‘Population’ sheet.

The series of data has 2000 values. For the purpose of this coursework we shall assume that this data represents the “population” with mean and variance given by = 22.5 and 2 = 2.25, respectively.

Click open the sheet ‘Task 1 allocated numbers’ and make a note of the number next to your ID/registration number. This number is the unique sample size n assigned to you.

To construct the first estimator 1, draw 30 random samples of size n from the population. You must save this file containing all the 30 samples and submit it via Moodle.

Note: You cannot be given any credit if you use any other number than the one assigned to you to do this coursework.

Open the Excel document Answers and click open the sheet named Task1. For each of 30 samples drawn, calculate the corresponding value of 1 as the mean of the n values generated in that sample and copy these values (30 in all) into the cells A3:A32 (colour coded green).

Similarly, to construct the second estimator 2, take another 30 samples each of size n/2 (e.g. if your sample size was 80 before, now it should be 40). For each of 30 samples drawn, calculate the value of 2 as the mean of the n/2 values generated in that sample and copy these values (30 in all) into the cells C3:C32 (colour coded green).

In cell E4 (colour coded green), type the number n given to you as the sample size.

i. What is the calculated bias of estimator 1? Write this number in cell G3 (colour coded yellow). (6 marks) 


ii. What, according to theory is the standard error of the estimator 1? Write this number in cell G6 (colour coded yellow). (3 marks) 


iii. In reality, the value of is unknown so the standard error of 1 has to be estimated. What is the value of this estimate given the sampling distribution of 1 you have calculated? Write this number in cell G9 (colour coded yellow). (6 marks) 


You need to repeat performing the above three exercises for the second estimator 2 as well. Thus,

iv. What is the calculated bias of estimator 2? Write this number in cell G12 (colour coded yellow). (6 marks)

v. What, according to theory is the standard error of the estimator 2? Write this number in cell G15 (colour coded yellow). (3 marks) 


vi. In reality, the value of is unknown so the standard error of 2 has to be estimated. What is the value of this estimate given the sampling distribution of 2 you have calculated? Write this number in cell G18 (colour coded yellow). (6 marks) 


vii. What is the relative efficiency of estimator 1? Write this number in cell G22 (colour coded yellow). (5 marks) 


viii. What, according to theory will be the difference between the bias of 1 and that of 2? In cell G26 (colour coded yellow) write the number 1 if the theoretical bias of 1 is smaller than that of 2, the number -1 (negative 1) if the theoretical bias of 1 is larger than that of 2 or 0 if this difference is zero. (3 marks) 
End of Task 1 


Task 2 (30 marks)

Task 2 is an exercise on two-variable regression. The independent variable is X and the dependent variable is Y

The population data for this task is in the Excel file Coursework Data, sheet named Data.
There are five columns of data. The first column has the data on the dependent variable GDP per capita (G).

The other four columns of data are on Electricity Consumption per capita (E), Fixed Broadband Subscribers (F), Improved water source (I) and Land area (L).

Click open sheet Task 2 and locate your ID/registration number. Find that the number of countries and the independent variable have been specified next to your ID/registration number.

Prepare your own data-set for this task as follows: Say the number next to your ID/registration number is 35 and the letter specified is I. This means that you should choose any 35 countries and the corresponding data on each of G and I.

Note: You should choose the countries manually but randomly. Do not use a random generating mechanism.

You must save this data-set file and submit it via Moodle.

Using notation, the variable G is to be denoted by Y in this task. The notation X will denote the specified independent variable – I in our example (which may not be independent variable in your case).

Important: It is absolutely necessary that you select the exact number of countries and the independent variable specified. Failure to do this is likely to cost you the marks allocated to this task.

Open the Excel document Answers and click open sheet named Task2. Write the number given to you in cell B3 (colour coded green).

Use a calculator to find the values of ƩX, ƩX2, ƩXY and ƩY. Write these numbers in the cells (all colour coded green) D2, F2, H2 and J2, respectively.

Suppose that the pair of normal equations is given as b0 = B - Ab1 ..... (1)

Cb0 +Db1 = E........... (2)

i. Write down the values of A, B, C, D and E in the yellow coloured cells B5, B7, B9, B11 and B13. (3 marks X 5) 


ii. Now solve the two equations above to obtain the value of the constant term of the fitted line of regression of Y on X and write this number in cell E15 (colour coded yellow). (8 marks) 


iii. Similarly solve for the slope term and write this number in cell E17 (colour coded yellow). (7 marks) 
End of Task 2 


Task 3 (32 marks)

Task 3 is an exercise on multiple regression – construction of a Confidence Interval and performing a Hypothesis Test

The population data for this task is in the Excel file Coursework Data, sheet named Data.
There are five columns of data. The first column has the data on the dependent variable GDP per capita (G).

The other four columns of data are on Electricity Consumption per capita (E),Fixed Broadband Subscribers (F), Improved water source(I) and Land area (L).

Click open the sheet Task 3 and locate your ID/registration number. Find that the number of countries and the independent variables have been specified next to your ID/registration number.

Prepare your own data-set for this task as follows: Say the number next to your ID/registration number is 45 and the letters specified are F, I and L. This means that you should choose any 45 countries and the corresponding data on each of F, I and L.

Note 1: Some of you have been asked to choose three independent variables and some four.
Note 2: You should choose the countries manually but randomly. Do not use a random generating mechanism.

You must save this data-set file and submit it via Moodle.

Using notation, the variable G is to be denoted by Y in this task. The notation X2, X3 and X4 will denote the three independent variables if you have been specified only three.
If you have been assigned four independent variables then these should be denoted by X2, X3, X4 and X5.

Therefore, the Classical Linear Regression Model (CLRM) is either

Y = 1 + 2X2 + 3X3 + 4 X4 + 
if you have been assigned three independent variables or is Y = 1 + 2X2 + 3X3 + 4 X4 +5 X5 + 
if there are four independent variables.

Important: It is absolutely necessary that you select the exact number of countries and the independent variables specified. Failure to do this is likely to cost you the marks allocated to this task.

Use Stata to run a multiple regression of Y on X2, X3 and X4 and a constant (if you have been assigned three independent variables) or on X2, X3 and X4 and X5 if you have been assigned four.

Task 3a:

Open the Excel document Answers and click open the sheet named Task3a. Write the number of countries in cell A3 (colour coded green). Write the number of independent variables you have been assigned (either 3 or 4) in cell E3 (colour coded green). Finally, write in cells J1 and J2 (both colour coded green) the estimated coefficient of the variable X2 and the estimated standard error of this estimator as given in the Stata regression output, respectively.

i. What is the degree of freedom of any t-statistic in your model? Write this number down in the cell E5 (colour coded yellow). (2 marks)

You will now construct the 90% confidence interval for the parameter 2. To do this you will first need the relevant t-value from the t-table corresponding to the degree of freedom in your model.

ii. In cell E8 (colour coded yellow), write down the t-value you have found from the t-table. ( 4 marks) 


iii. In cell E10 (colour coded yellow), write down the lower limit value of the confidence interval for the parameter 2. ( 6 marks) 


iv. In cell E12 (colour coded yellow), write down the upper limit value of the confidence interval for the parameter 2. ( 6 marks) 


Task 3b:

Open the Excel document Answers and click open sheet named Task3b. Write the number of countries in cell A3 (colour coded green). Write the number of independent variables (either 3 or 4) in cell D3 (colour coded green). Finally, write in cells J1 and J2 (both colour coded green) the estimated coefficient of the variable X3 and the estimated standard error of this estimator as given in the Stata regression output, respectively.

You will now test, at 5% level of significance, the hypothesis that the variable X3 has a positive effect on Y. To do this you will need to calculate the t-statistic as discussed in the lecture/lab session.

i. In cell D6 (colour coded yellow), write down the value of the t –statistic you have calculated. ( 3 marks)

You will also need the relevant critical t-value corresponding to your test. Find this value from the t-table.

ii. In cell D10 (colour coded yellow), write down the critical t-value you have found from the t-table. ( 5 marks)

You will now reject or retain the null hypothesis by comparing the t-statistic with the critical value.

iii. In cell D12 (colour coded yellow), write down either reject or retain to denote the conclusion of your test. ( 6 marks)

End of Task 3