Correlations and regressions are both methods used to determine and measure connections between variables. Variables are the data we have. With some business statistics help we can find these connections.  For example, one variable might be the shoe sizes of everyone in the class and another might be our height. Shoe size and height would be the variables. Finding connections between variables can help businesses make better decisions. We would assume that opening an additional location for our business would increase sales. But what are the connections between sales and the size of the store, the number of employees working there, or even the colors used in decorating the store?  Knowing these connections can help businesses make better decisions as the business grows.

Correlations and regressions provide this type of information to managers, lenders, and anyone working in or with the business.

There are several ways to display quantitative data, the first is called a stem-and-leaf plot.  They are examples of exploratory data analysis, which was developed by John Tukey in 1977.
 In a stem-and-leaf plot, each number is separated into a stem and a leaf.  Each leave represents a single point of data within the set.  Each leaf should be a single digit therefore.  A stem-and-leaf plot is comparable to a histogram but still contains the original data values.  It is a very quick and efficient way to sort and organize data to view.       
           
For example, lets say you measured how old everyone in the room is and the results were as follows:
7, 18, 29, 42, 45, 54, 56, and 59

The stem-and-leaf plot would look as follows:
0|     7                                      Key:    5|     3   = 53
1|     8
2|     9
3|
4|     2   5
5|     4   6    9

Using the key provided, we can see that the stems represent values of 10.  So 2| would indicate in the 20’s.  By plotting the points this way we can clearly see it is skewed to the left (since the results are very highly represented within the 40’s and 50’s) and the median value is 45. 

Another way we can graph is with linear regression.
 The equation of a line is known as y= mx + b;
Where y=  Dependent variable
x= Explanatory variable
m= Slope
b= Y intercept.

To put this into perspective and provide you with some business statistics help, I can provide an example of linear regression in action.

Participants were asked to write their shoe size and their age.  Let Age be represented by x and Size be represented by the variable y. 

Age:                                                    Shoe Size:
11                                                        5
12                                                        7
13                                                        9
14                                                        11

Now we can plot each of these points on a graph to find the correlation between the X and Y variables.



To find the equation of the line first we must find the slope.
Grab any 2 points within the data, in this case I am going to use (11,5) and (13,9).
Slope is calculated as y2-y1/ x2- x1
(9-5) / (13-11) =  4 / 2=  2

So our slope is calculated as 2 and our equation looks like this:
y= 2x + b
All that’s left is b!

Simply grab any point and plug it into the new and improved equation.  I will use (12, 7) and solve for b.
7= 2(12) + b
7=24 + b
b= -17

Now we can see our full equation of the line!
y = 2x – 17

Lets plug in the final point, (14,11), to test our equation
y= 2 (14) – 17
y= 28 – 17
y= 11 PERFECT!