# statistics

a training manager wants to know if there is a link between the hours spent by particular category of employeee in training and their productivity on the job. a ssmple of 10 employee files was randomly selected and the following data extracted:
employee productivity hrs in training
1 45 16
2 70 36
3 44 20
4 56 38
5 60 40
6 48 30
7 75 35
8 60 22
9 63 40
10 38 24

1.set up a regression line to establish a linear relationship between productiity and training hours for these eployees.
2.Establish the productivity level for an employee who received 21 hours of training.
3.determine the coefficient of correlation between productivity and the hours of training. advise the training manager on your findings

You can do this directly using a calculator with linear regression, or using excel.

Either of these will give you m (gradient of line) and c (intercept)

Using excel I get

y = 0.8865x + 29.215

where y is productivity and x is hours in training.

So for 21 h training I get a productivty level of 31.

I have done this rather quickly so check my working as I may have typed numbers incorrectly.

It is much easier to do these kinds of problems using calculators, but if you are expected to do them by hand, here are a few steps you can use:

Regression equation is predicted y = a + bx
...where a represents the y-intercept and b the slope.

To get to that point, here are some formulas to calculate along the way.

To find a:
a = (Ey/n) - b(Ex/n)

Note: E here means to add up or to find the total.

To find b:
b = SSxy/SSxx

To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n

To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n

To determine correlation coefficient, here is a formula:

r = n(Exy) - [(Ex)(Ey)] divided by SQRT of {[n(Ex^2) - (Ex)^2][n(Ey^2) - (Ey)^2]}

Note: I'm using SQRT to mean square root.

It may help to set up a table of values. Make a column for X values, Y values, X^2 values (^2 means squared), Y^2 values, and XY values. Total each column. Note that XY means to take X * Y for each pair of values. X^2 means to square each X value. Y^2 means to square each Y value. The value n in all formulas is 10 (for sample size and based on 10 data pairs). Once you have all the values you need for the formulas, just plug the values into the formulas and go from there.

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