Data Analysis #6: Simple Linear Regression

[samvara]

Test back (74%) and an hour talk on resources available in the Business Library by one of the staff.We also covered some of the many databases available to people looking to acquire a large, interesting dataset.

• Australian Bureau of Statistics
• Passport GMID (UWA portal only)
• DatAnalysis (UWA portal only)

Chapter #8: Confidence Interval Estimation

Talked about how to use PHStat and Excel to work it out for you and how you can reverse engineer from the confidence you need to work out your minimum sample size.

The (Student) t Distribution:

• Using the alias Student, W.S. Gosset, chief brewer for Guinness in Ireland, published the first paper using the t distribution to assist in quality control procedures (via CIs) at the brewery.
  
• In appearance, the t Distribution resembles the normal distribution. However, it has more are in the tails and less in the centre than the Normal Distribution.
• As the number of degrees of freedom (df=n-1) increases, the t Distribution gradually approaches the Normal Distribution.

Using the table is pretty simple... if you want a confidence interval of 90% (i.e. 5% at either end) and sample size is 3 then std dev/2 = 0.10/2 = 0.05 and df = n - 1 = 3 - 1 = 2.

Student's t table

df	0.25	0.10	0.05
1	1.000	3.078	6.314
2	0.817	1.886	2.920
3	0.765	1.638	2.353

Examples of how to use output from PHStat and Excel.

Chapter # 13: Simple Linear Regression.

• relationship between variables is described by a linear function
• change of one variable is a major factor in change on the other
• dependency of one variable on the other
• regression based on principle of least squares
• provides an estimate of population regression line as well as a predicted value of Y

Example: Examine the linear dependency of annual sales versus size of stores

Store	Metres squared	Annual Sales ($000)
1	1726	3681
2	1542	3395
3	2816	6653
4	5555	9543
5	1292	3318
6	2208	5563
7	1313	3760

Analysis: Can do a scatter diagram and generate a sample Regression Line

• Y = 1636.415 +1.487X

Where Y is Annual Sales and X is floor space - obviously this has certain limitations; for a start it implies you can make $1,636,415.00 annually if you have zero floor space.

• Only applies between upper and lower boundaries - can't use this to predict above or below.

We can, however, assume that within these boundaries for an increase in 1 unit of floor space, we get a sales increase of $1,487.

...and then we ran away