Table 1 Innovation in the Mobile Phone Industry
Company Proportion of Sales Revenue from New Products %
1 27.4
2 15.7
3 85.34
4 94.2
5 60.0
6 57.5
7 13.4
8 8.0
9 0.0
10 33.6
11 15.7
12 100.0
Calculate the mean, mode, median, minimum, maximum, range, variance and standard deviation and present them in a single table.
Based on this sample of 12 companies and using the measures derived in (a) write a short report for the government on innovation in the mobile phone market commenting on the average and median proportion of sales from new products, the most and least innovative companies, variance in the share of sales from new products and the impact of any outliers. Discuss the strengths and weakness of the different measures.
Guidance: For part (a) show your calculations step-by-step using Tables provided in the lectures and tutorials. For Part (b) discuss the measures in the context of the Mobile Phone Market e.g. rather than saying “the average is X”, it is better to discuss this finding in context by saying something like, “On average Mobile Phone Companies in this sample derive X per cent of their sales from new products” and so on. This adds relevance and meaning.
Answer ALL parts of this question.
Share prices on the National Stock Exchange of India are normally distributed with a mean of 126.5 and a standard deviation of 15.8
Explain how the z-score can be used to determine the probability of observing a given rate of return?
Calculate the probability that a company’s share price exceeds 150
Calculate the probability that a company’s share price is less than 100
Answer ALL parts of this question
Table 2 below presents data on sales revenue and marketing expenditure for a sample of companies in the personal computer industry. The industry trade association has asked you to test the hypothesis that there is a positive relationship between Advertising Expenditure and Sales Revenue. Using the data in Table 2 answer parts (a) to (e) below.
Table 2 Advertising Expenditure and Sales Revenue in the Personal Computer Industry
Company Advertising Expenditure
£million Sales Revenue
£million
Company 1 1.8 216
Company 2 1.1 125
Company 3 6.4 983
Company 4 8.2 1361
Company 5 4.3 753
Company 6 14.5 2461
Company 7 4.6 645
Company 8 5.7 688
Company 9 1.8 321
Company 10 7.2 972
Set out a null hypothesis and an alternative hypothesis regarding Advertising Expenditure and Sales Revenue.
Calculate Pearson’s correlation coefficient between Advertising Expenditure and Sales Revenue.
Use a t-test to determine the statistical significance of the correlation coefficient attained in (b) above.
Comment on the distinction between correlation and causation.
In light of the results attained above, what advice, if any, would you give companies seeking to increase their sales revenue?
Guidance
Please show your calculations clearly step-by-step and use a Table as we did in class. Marks are awarded for clear exposition of the derivation and explanation of your results.
SECTION 2 (30 Marks)
Marks will be awarded for clear verbal explanations and clear step-by-step calculations.
4. Answer ALL parts of this question.
You have given the following time series data on R&D expenditure as a proportion of GDP and Patents Granted in the Mechanical Engineering sector in South Korea.
Table 3 R&D/GDP (R&D) and Patents (P)
Year R&D/GDP (%) Patents Granted
2008 1.96 3007
2009 1.95 2950
2010 1.98 2500
2011 2.5 3600
2012 1.3 1600
2013 1.2 1500
2014 1.9 2578
2015 2.4 3546
2016 1.5 1750
2017 2.5 3478
2018 2.7 3896
2019 1.6 1893
The relationship between Patents, P, and R&D/GDP, R&D, is assumed to be given by the following linear model:
Pt = β1 + β2R&Dt + ut
Calculate estimates of β1 and β2 using the Ordinary Least Squares (OLS) regression method. Show you calculations step-by-step.
Consider the estimate of the constant term β1 and discuss whether it is significant and meaningful. (Note that the standard error of the estimate of β1 is 222.898).
Consider the estimate of the slope coefficient β2 and discuss its size, sign, significance and meaning. (Note that the standard error of the estimate of β2 is 110.686).
The figure attained for adjusted R2 is 0.955. Explain the meaning of the adjusted R2 statistic and comment on its size.
e) How might you improve on the above model and results?
SECTION 3 (50 Marks)
Please read the questions and guidance carefully before your start. Please note that this is an individual assignment and you should not share you work or results on hours and part-time work with others – there is, plenty of opportunity to discuss other regression models in the tutorials.
3. You have been asked to carry out statistical analysis to shed light on whether the hourly earnings of part time employees are less than those of full-time employees. Please provide a report on how the number of hours worked per week affects earnings. Your report should include the following:
A brief review of the literature on earnings and part-time work. You should carry out a literature search using the Web of Science database via the SOAS library homepage.
Calculate the average earnings of those working 40 per week or more and compare it with those working less than 40 hours per week, using the Dougherty dataset and briefly discuss your findings.
Bi-variate Regression
Based on your reading of the literature, set out a simple bivariate model and a null and an alternative hypothesis to test whether hours worked has a significant impact on earnings. Comment on the appropriateness of using a one-tail test in this case. Estimate your bivariate model using OLS in SPSS. Present and discuss your results, commenting on the size, sign and significance of the beta coefficients and the goodness of fit of the model. Discuss the limitations of the results, including omitted variables bias.
Correlation Matrix and Multi-variate Regression
Based on your wider reading of the literature under (a) discuss other explanations, in addition to hours worked per week that may explain earnings, for example, education, sector of employment, experience, age, gender tenure and so on. Present the correlation matrix for these variables and discuss your findings commenting in particular on potential issues of multicollinearity.
Specify a multiple regression model to test hypotheses by selecting additional explanatory variables to add to your model. Estimate your multivariate model using OLS and discuss your results and comment on the size, sign and significance of the beta coefficients and the goodness of fit of the model. Does the impact of “hours worked per week” persist after adding/controlling for other variables?
Discuss possible problems, such as multicollinearity, heteroscedasticity and simultaneous equations bias. Carry out diagnostic tests/explorations for multicollinearity and heteroscedasticity.
