Tutorial 11 in week 12 PDF

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Tutorial Guide Every week, there is a new lecture and a tutorial that covers material from the previous week. Before going to a lecture, students are advised to go a tutorial reviewing what they have learnt from the previous lecture and preparing for the next lecturer. Tutorials are an integral part of developing skills in business statistics and data analytics. Without practice, understanding of key concepts in this subject and implementation of key techniques cannot be achieved. This will hamper the future study of other subjects, such as finance and economics. You should turn up to your tutorial – the one you have been allocated to. Rooms, including Zoom ones, cater for only a certain quota of students so overcrowding occurs when people just turn up to any tutorial. By turning up to a tutorial that you shouldn’t be at, you will be disrupting the learning of students who have the right to be there. Tutorial staff can only deal with and attend to a certain limited number of students. If you do wish to change your tutorial, you must do so online via the MyStudent / OneStop Admin. Please don’t ask the Business Statistics staff to change tutorials because they cannot make those changes. If you do prepare for tutorials, you will have several outcomes: 1. 2. 3. 4.

You can confirm your learning achievements. You can amend your learning of topics that you may have minor misunderstandings. You can identify where you need to spend more time reviewing. Tutors can move through easier material that everyone is OK with more quickly.

and this means a chance to expand on more problematic areas and to have a better idea what major you want to choose in the next year. If you do not prepare, you will fall behind as the tutor will cater to those whom have prepared. You will think that everything needs reviewing and start freaking out! Remember, you should devote 6 hours per week to Business Statistics outside of the 3 hours face-to-face contact you have in the form of lectures and tutorials. You should bring the following to tutorials: 1. 2. 3. 4. 5.

Tutorial question sheet and your attempt at the answers to each question Lecture notes and study notes Textbook (optional) Calculator Pens/Pencils and Paper/Exercise book

Tutorial 11 in Week 12: Regression Analysis II Question 1. Jones&Johnson is a supermarket selling locally sourced organic vegetables and meat products. The manager of Jones&Johnson is interested in how investment in advertising helps with boosting its sales. The manager collected a random sample of quarterly sales (in 100,000 dollars) with the amount of investment in TV advertising (in 10,000 dollars), newspaper advertising (in 10,000 dollars) and the average price change in that quarter (in dollars). The average price change is measured as the difference between the average price of its products in one quarter and that in a previous quarter. The manager ran a regression of quarterly sales on the other variables and she obtained the following output.

The Manager suspects that the model not adequate in capturing the variation in sales. She decided to add another variable: the quarterly sales of a competitor. After adding this variable, a new regression was run and the manager obtained the following table of regression summary.

What is the problem with adding this new variable? Do you recommend the manager to use the regression with the newly added variable? Question 2. Question 2. If two employees perform the same task competently, their wage should be the same, differing only in relation to the number of years of experience (or seniority) that they have. Factors such as race, gender or educational level should not play a

role in determining the wage they earn. To test if the latter three factors do in fact play a role in determining wages, a random sample of workers at an assembly line of a factory where all workers perform the same job is collected. The following coding is used for the dataset. Gender: female = 1, not-female = 0; Race: Caucasian = 1, non-Caucasian = 0; Education: with a university degree = 1, without a university degree = 0. 1. Looking at the scatter plot between hourly wages and number of years of working experience,

do you think the following regression model is a sound one? What needs to be added and why?

y i=β 0 + β 1 x 1 ,i + β 2 x 2 ,i + β 3 x 3 ,i + β 4 x 4 , i+ ϵi

where ϵi ∼ N (0 , σ ) is a normally distributed error term y i is the hourly wages of worker x 1, i

i (in dollars)

is number of years of working experience of worker i

x 2, i is a dummy which equals 1 if worker i I female and 0 otherwise x 3 ,i

is a dummy which equals 1 if worker i is Caucasian and 0 otherwise

x 4 ,i

is a dummy which equals 1 if worker i has a university degree and 0 otherwise

2. A quadratic term is added and the following regression result is obtained.

At the 1% level, test if the variable number of years of working experience has diminishing marginal effect on hourly wages 3. Write down the estimated model. 4. Interpret the intercept. 5. Interpret the coefficient of Gender and the coefficient of Education. 6. At the 5% level, what types of payment inequality are significant? 7. Predict the hourly wages for a male Asian worker with no university degree and 5 years of working experience.

Question 3. Empirical asset pricing studies the determinants of the stock price of any publically listed firms based on firm characteristics. A random sample of monthly stock prices of a firm is collected together with selected firm characteristics. A regression analysis shows the following result

based on the regression model y i=β 0 + β 1 x 1 ,i + β 2 x 2 ,i + β 3 x 3 ,i + β 4 x 4 , i+ ϵi

where ϵi ∼ N (0 , σ ) is a normally distributed error term y i is the natural logarithm of monthly stock price (in dollars) in month i x 1, i

is the natural logarithm of sales (in 10,000 dollars) in month i

x 2, i is the amount of short-term debt (in 10,000 dollars) in month i x 3 ,i is an interaction term between the natural logarithm of sales in month amount of short-term debt in month i , i.e. x 3 ,i= x 1 ,i × x 2 ,i

i

and the

x 4 ,i

is a dummy variable which equals 1 if the firm is overvalued, and 0 if the firm is undervalued. 1. Suppose there is no interaction term (equivalently suppose β 3=0 ). Interpret the coefficient on x 1, i . 2. Keeping book-to-market constant, what is the expected effect on stock price that a 2% decrease in sales has, for a firm with 15,000 dollars in short-term debt? 3. Predict the stock price of an overvalued firm with 250,000 dollars in sales, and 15,000 dollars in short-term debt....