Order 1407348: (statistics) use your own ingenuity in constructing an interesting hypothesis, and finding the relevant data before conducting the analysis

1

Assignment: Quantitative Methods 2 The following assignment is designed to give you a first experience in conducting original empirical

research. You will have to use your own ingenuity in constructing an interesting hypothesis, and finding the

relevant data before conducting the analysis. This exercise should assist you in understanding the statistical

components of the course and in building skills that will be useful in completing your 3rd year dissertations.

The Task

To complete this assignment you must find two or more variables that you believe are related, one of which

is to be explained by the others using an OLS regression, ANOVA or PROBIT regression;

The data may be found anywhere on the web or in books, journals or magazines in the library1. You are free

to do any topics that is of interest to you. It need not be directly relevant to your course. The only

limitations are that:

 The data must be secondary (it cannot come from a survey that you conduct yourself);

 The data must not already been analysed in a similar way to the way you propose;

 The sample size must be at least 25 observations (for all variables)

 Your analysis needs to be yours and must be different to others in the class. The same data set can be used but if two students present essentially the same analysis then this will be looked at

very closely to verify that it is original.

 It cannot be from the data sets provided to you on BB.

You are recommended Python but you can use Excel or other software if you wish. Then:

I) Complete a report summarising the analysis; and,

II) Present copy of the data and a copy of the results of the analysis.

Within the report you must complete the following objectives within (I):

1. Clearly state what hypothesis or hypotheses are to be tested, and write one or two paragraphs on why you believe that the analysis is worth doing with supporting evidence from literature

(e.g. textbooks, articles or internet).

2. Give an exact source for the data. This must be a verifiable source so that we can check if the data is genuine.

3. Present a summary analysis of the results, with a formal test of the appropriate hypothesis using the data.

4. It should contain references if they have been cited within the text.

 The failure to attach the data in full along with a verifiable source, or a full set of regression results that can be clearly read will result in 0 mark being given.

 Full criteria for Marking are given in the attached Rubric at the end of this document

 Assignments should not exceed 1000 words (excluding graphs tables and references). .

The material necessary to complete this assignment will be completed late in the Autumn Term. Data

should be obtained prior to the Christmas break. However, you will need to submit the assignment

electronically, and will be in due on Monday 14/1/2019.

Note that you should expect your marks back on the Friday 01/2/2019 to be within the 15 day

deadline.

1 You are free to find whatever data you wish. If you lack ideas, simply GOOGLING the words “data” on “marketing” or “food consumption” etc will get a very high number of hits. Sites run by DEFRA (http://www.defra.gov.uk/) the food

(http://www.food.gov.uk/) Standards Agency contain reports with interesting data. However, there also sites that have links to a

multitude other data sets. For example, http://www.economicsnetwork.ac.uk/links/data_free.htm. Another site is FRED

https://fred.stlouisfed.org/ where you will find mountains of data

.

2

An Example: Below is a decent assignment but could have been made better. The underlined

comments in red are notes to this effect.

1. My Hypothesis

My hypothesis is that the consumption of beef depends upon the price that it is sold. Economic

theory suggests that as the price of beef rises the quantity of beef that is demanded by consumers

will fall. Such effects have been recognised in the literature (e.g Rutherford, 2018).

 More credible references to support this would have been useful… or any previous analysis on this topic).

Therefore, a regression of the following form will be conducted:

ln(Demand for beef) = constant + slope *ln (Price of beef).

 (Ok, but a pretty simply bivariate relationship, there might be other forms that could be investigated or other variables added to the right hand side. It’s also a rather generic sort

of example and not particularly innovative)

This analysis is useful because it will quantify the extent to which the demand for beef is dependent

on price and we will also be able to test the hypothesis that “slope” is negative (that the demand

curve is downward sloping). I will test this hypothesis, by stating my null hypothesis as: H0:

slope=0 against the alternative hypothesis H1: slope<0.

 (I probably should have considered and discussed the potential pitfalls of using the data an model. For example, why might the slope not be downward?)

2. Data

The demand data was obtained from the web (the source web address or exact reference to a book

including page number should have been used). This data is presented in the attached page. The

quantity of beef and price of been is for 100s of kilograms, and represents the amount of beef

purchased in 25 UK supermarkets over the same period. The price is the average price per

kilogram.

 (I did not mention exactly when the data was collected or by whom).

3. Analysis

The regression analysis is presented in the attached page that also contains the data. From these

results, we have following the estimated relationship

ln(Demand for beef) = 5.07 - 0.277*ln (Price of beef).

Therefore, as the logged price of beef goes up by one pound per kilogram, the logged demand for

beef in these supermarkets is predicted to fall by .277 units. The hypothesis that the slope is 0

cannot be rejected at the 5% level of significance, in favour or the alternative that there is a

downward sloping demand curve, since the two tailed significance level is 0.365 and the one tailed

significance is approximately 0.182 (0.365/2 ) which is greater than 0.05.

 (I missed something here, the dependent and the explanatory were logged, which means that the relationship was not linear and the coefficients were therefore elasticities. That

should have been discussed )

 I did not discuss the intercept, this was not that important but worth mentioning.

 I failed to find a significant relationship but did not comment on why this might be The R-Square value of .035 suggests that only around 3.5% of variation in beef consumption was

explained by prices.

 (I could have noted a bit more about whether I thought this was low and high and why)

 (A scatter plot might have been useful here)

3

 (The results here confirmed my initial expectations in terms of the sign of the coefficient but I did not discuss that, nor did I have any comparison with existing work: which for this

example exists since a lot of previous work has been done on the demand for beef).

References

 Ruthorford B. (2018) Does beef demand impact on you? https://www.beefmagazine.com/commentary/does-beef-demand-impact-you

4

The data is:

lndemand lnprice

1 6.084304 1.000366

2 2.531097 -0.38109

3 5.096382 -0.37567

4 5.732355 -0.07447

5 2.749785 0.433496

6 4.171341 1.278379

7 5.240121 -0.63468

8 5.570505 0.508396

9 6.140155 0.216116

10 5.525414 -1.85861

11 3.82514 -0.41932

12 6.4334 -0.13233

13 6.237671 -0.03957

14 4.374993 0.326003

15 6.37105 -2.04032

16 5.358738 0.046256

17 5.905113 -0.67768

18 5.923927 -1.43944

19 6.144548 0.524296

20 2.894401 0.73528

21 6.367449 -0.65325

22 4.959244 0.842456

23 4.973623 -0.38152

24 6.140287 0.066489

25 3.205766 -1.09874

5

The output is: ____________________________________________________________________

Rsquared 0.03579

( 3.58 % of the variation in the dependent variable can be explained

by the independent variables)

____________________________________________________________________

Test for Null (H0): ALL the regressors having a zero slope (i.e. No

Regression)

F-Value P-Values

No Regression 0.853722 0.365094

The NULL (H0) CANNOT be rejected at the 10% level of significance

____________________________________________________________________

Model Coefficients

Coef. P-Values Std.errs t

Intercept 5.071293 0.000000 0.252073 20.118328

lnprice -0.277714 0.365094 0.300566 -0.923971

6

Indicative Marking Criteria Presentation Poor Adequate Good

Word Limit Not Observed

Observed

Underlying Hypothesis Poor Adequate Good

Motivation and explanation of the hypotheses Poor Adequate

Supporting materials for the hypothesis Absent Used Extensive

Expected Sign of the Coefficients Not Clearly Stated

Clearly Stated

Structure of Assignment Poor Adequate Good

Data Inadequate Adequate

Data Source Unclear Clear

Full Table of Results Attached Not Attached

Analysis (Coverage) Incomplete Complete

References Included (if Applicable) Incomplete N/A Complete

Analysis (Clarity/Accuracy)

Explanation of R Square Missing Inaccurate or Unclear

Accurate and Clear

Explanation of Coefficient/Parameter Signs and Magnitudes

Missing Inaccurate or Unclear

Accurate and Clear

Formal Statement of Hypotheses Missing Inaccurate or Unclear

Accurate and Clear

Use of P Values and testing of hypotheses Missing Inaccurate or Unclear

Accurate and Clear

Discussion of Results (In the light of initial expectations)

Missing or Poor

Adequate Good

Note: the overall mark is not a sum of its parts. A distinction mark (70+) would normally require all

components to be done to a high level. Marks are not allocated to individual components. You should

understand that you start from 0 and work up. You do not start from 100 and work down. Particular

emphasis should be given to correctly conducting inference using P-Values. Work that does not accurately

conduct appropriate inference using P-Values will not receive a first class mark.