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**Soph.****Guest**

Help meee! I need to hypothetically show my findings to the 'board of directors' in one week's time. But what findings? I think i need to find the correlation between things, but what? I dont know what is relevant and what is not. Im really stuck if anyone can help!

Thank alot!!!

Cow Industrials Ltd is a medium sized Engineering Company based in the North East. A number of their regular customers have made complaints over the last few orders they have received from Cow Ltd. These complaints can be summarized as follows:

Products have been of a substandard nature

Products are arriving late

A combination of the above products have been of a substandard nature and have arrived lateSome of the customers have threatened that if this continues, then they will cancel their future orders and find another local supplier.

Consequently, the Managing Director has asked the Production Manager to investigate this immediately. He has replied, saying that he cannot meet production and deadline targets, because a large number of his workforce is constantly absent. He has done some basic statistical calculations and says there is strong correlation between production and workers attendance. Clearly something must be done about this, as the company does not want to lose their valued customer base.

The company has therefore called you in, the Information Analyst, to help the Production Manager. You are being asked to give advice regarding the absenteeism of the production workforce, and your brief is to analyze certain factors to try and reduce this high absenteeism and therefore increase production.

After an initial discussion with the Production Manager, you have decided to take a representative sample of ten employees and look at three possible factors the age of the employee, their holiday entitlement and their hourly rate of pay (grade) - that may affect absenteeism. The Production Manager has given you the required data for each employee in your sample (see overleaf):

EMPLOYEE DAYS PAY HOLIDAY AGE ABSENT SCALE ENTITLEMENT (Days)

A 12 B 25 18

B 14 C 25 57

C 10 B 25 44

D 18 C 20 32

E 6 A 30 21

F 4 A 30 19

G 20 E 20 23

H 19 D 20 39

I 28 E 15 45

J 7 B 30 52N.B. Employees are paid different hourly rates depending on their grade. These are as follows:

Grade A - £ 10.00 per hour

Grade B - £ 8.00 per hour

Grade C - £ 7.00 per hour

Grade D - £ 6.00 per hour

Grade E - £5.00 per hour

Grade F - £4.75 per hourIn a weeks time, the Production Manager and Managing Director will be asking a variety of questions regarding the above data. You are therefore advised to comprehensively analyze this data and bring your calculations and findings with you.

**Soph.****Guest**

EMPLOYEE DAYS PAY HOLIDAY AGE

ABSENT SCALE ENTITLEMENT

B 14 C 25 57

C 10 B 25 44

D 18 C 20 32

E 6 A 30 21

F 4 A 30 19

G 20 E 20 23

H 19 D 20 39

I 28 E 15 45

J 7 B 30 52

The table should look a little more like that^ hehe

**Zmurf****Member**- Registered: 2005-07-31
- Posts: 49

I think some of the data from the table is missing, or I'm not reading it right.

EDIT: Oh I see now.

*Last edited by Zmurf (2006-05-10 00:33:01)*

*"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."*

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**Zmurf****Member**- Registered: 2005-07-31
- Posts: 49

The first thing I notice is the link between pay scale and days absent. There pay scale is inversly porportional to the days they are absent. Employee I just needs the sack by the looks of things.

Is this a real company or a hypothetical maths question?

*"When subtracted from 180, the sum of the square-root of the two equal angles of an isocoles triangle squared will give the square-root of the remaining angle squared."*

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,315

AbsentDays= 48 -1.425Holidays

(2.388) (0.0975) R²=0.964

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,315

(H0) If the (original )coefficient of holidays is 0, while its sample standard deviation is 0.0975, then according t distribution for degree of freedom being 10 (Samples Size)-2 (Coefficient Amount)=8, -1.425/0.0975 should be at the very tail of the bell curve. Thus the probability for a sample observation of a 0 coefficient, -1.425/0.0975, to occur is very low. Usually they integrate PDF before -1.425/0.0975 and double it for symmetricity of t distribution to demonstrate how low the "altogether" probability is and say it's an almost imposible event.

Since its probability is too low under the assumption that the coefficient is 0, we have enough reason to doubt the very assumption. This is like what cops do-yes the victim can die of an accident but the situation is unnormal and the probability for an reasonable accident in that situation is too low, thus a further investigation should be compulsory.

Refusing 0 assumption= admitting non zero= admitting that there is a correlation between AbsentDays and Holidays-we can interpret it as lack of Holidays being cause and absent behavior being effect. And -1.425Holidays is called statistically significant.

Initially I used excel (tools-data digging-regression, load vb before first using) to do the regression of absent days to 3 other variables (grades turned into wages), but 2 of the 3 independent variables doesn't pass the 0 test-their integrated probabilty is more than 10%. Then I used only the remaining independent variable, also the significant variable Number of Holidays to do the regression and get post #5, with R²=96.4%, virtually as same as the previous R²=97.6%. So I could say this new function with variable amount reduced to 1, can explain as much dependent variable, the amount of absent days, as the previous function with 3 variables, why not choose the new one? Both my econometric textbook author and I believe in Occum's Razor, and I give you the simple function(formula).

**X'(y-Xβ)=0**

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