BILL Gates dropped out of Harvard University. But it didn't seem to slow him down. He still became the world's richest person.
It got me thinking: Do people with more years of education really make more money? If so, how much more?
Here is an even harder question: Will more education make you happier?
These seemingly impossible questions can be answered.
Here is how: First, get hundreds of bits of data. It will all be jumbled up and make no sense. But never mind.
You can straighten it out using a magical statistical technique: Regression analysis.
Simple
It is easy. All you need is an Excel spreadsheet to input the data. Then, you push the 'enter' button. The computer does the rest.
Our oldest daughter tried it and said, "Pretty cool".
She surveyed classmates at her school and found that students who watch TV spent less time studying.
No surprise there. But her regression also showed that computer games and chatting with friends showed no relation to study time.
Okay. That convinced Mrs Money and me. Now, we only limit TV time for our daughters. Computer games and chatting are okay.
In 1937, economist Irving Fisher hired dozens of employees who used mechanical adding machines to do regression analysis. It took weeks to solve a single problem. Today, computers do the same thing in less than one second. It is almost too easy. We risk taking it for granted.
When I am not writing the Doc Money column, I teach economics and statistics at Singapore Management University (SMU). My classes just completed a contest among 200 students. Each team chose "a very important question to answer with regression analysis". Here are the winners:
GOLD MEDAL
Do sports teams that pay their players high salaries win more games?
Students: Ding Chen, Teng Mengfei, Lin Ripeng, Hu Xiaowei.
Data: The player salaries and win/loss records for 31 NBA basketball teams were taken from the website www.nba.espn.com.
Regression result: Player salaries make absolutely no difference to a team's win/loss record.
It shows most teams could get away with paying players much less and win just as many games.
Prof's comment: A wonderful extension to this study would be to see if it applies to football as well.
SILVER MEDAL
Do the number of days spent shopping increase one's general level of happiness?
Students: Natasha Lim, Michelle Loh
Data: Survey of 200 shoppers by the authors.
Regression result: On average, each additional day of shopping per month will increase one's happiness by 12 per cent.
Prof's comment: Go shopping. Get happy.
Excellent work.
BRONZE MEDAL
What is the relation between sexual frequency and satisfaction from sex?
Students: Benjamin Loong, Zheng Huiweng, Tang Yen Hui
Data: Durex survey of 317,000 respondents from 41 countries at www.durex.com.
Students selected a subset of 20 countries. It showed the frequency of sex was highest in Greece and Spain. It was lowest in Japan. Singapore was in-between.
Students noted that frequency data may be upwardly biased since persons who are more active are more likely to respond to the survey.
Regression result: A doubling of monthly frequency results in a 38 per cent increase in satisfaction from sex.
Prof's comment: I had better not comment.
Excel at it
REGRESSION analysis using Excel is easy. Try this:
- Go to Tools and then Add-Ins. Tick the box 'Analysis ToolPak'.
- Next, go back and click again on Tools. A new option will appear: 'Data Analysis'. Hit it. Then choose Regression.
- Now, you are ready to find the relation between anything and anything else.
