Some general directions

• When you have a large data set, you need to know what kind of information this data set may provide you.
  
  
• Start thinking what relations (logical / mathematical are involved).
  
  
• The given data are explicit to you – what additional data/information you may generate? (implicit information)
  Usually, this information is much more important than what you have to start with.
  
  
• Start thinking what is important for you to know about the entire set of data you have (explicit & implicit)
  
  
• Utilize the DATA/SORT command to reorganize your data in ways that are important to you.
  
  
• Use Scatter/Bar/Line/Pie graphs to explore you data and then demonstrate your points.
  
  
• Sometimes, when you use Scatter graph you may want to add the trend line and identify the mathematical formulation as well the R². You may also want to try several versions of trend besides the linear if this is appropriate. Then you should explain what all this information means.

Remember,

real business people

deal with real business data

that may represent (or hide - and you have to uncover) real problems

that you need to find solutions for them and

manage their implementation.

NOT all textbooks have a “love” for reality, and their examples are based on and “fake” data. If this is a case, you cannot draw any “real” conclusion, and you can just expose the irrationality of your data. and you can provide real

View the BMCC video

http://www.bmcc.cuny.edu/news/news.jsp?id=590

A review of your basic algebra skills using Mathematica 7 is available in a related file.
It is important that you can understand the meaning of a line.
The equation relates variable x (horizontal axis) to y (vertical axis) with a line given by the equation:

y = a + b x

a provides the distance that the line intersects to the vertical axis.
If a is negative then the intersection is below the origin point (0,0),
if a is zero then it crosses the origin point (0,0), and
if a is positive then the line intersects to the vertical axis above the origin point.
This magnitude provides the value of y that is independent of any value of x, in other ways when b is zero.

If b is zero, the equation is reduced to y = a.
If b is positive, then the line has an upward slope.
That means that as the a increases, so y, and the value of b, the slope of the line indicates how x affects y. If the slope is 45o then any change of x results equal change in y.
If the slope is greater than 45o, any change of x results greater change in y, while if the slope is less than 45o, the change of x results smaller change in y.
If b is negative, then the line has a downward slope.
That implies substitution, as the value of x increases, the value of y decreases.


Manipulate[Plot[a + b x == c, {x, -10, 10}],
{a, -20, 20}, {b, -.01, .6}, {c, -10, 10}]



When we move from a 2D to 3D we have:

y = a + b x + c z

Manipulate[Plot3D[a + b x + c z == 0, {x, -10, 10}, {z, -10, 10}],
{a, -20, 20}, {b, -5, 5}, {c, -5, 5}]

Now we do not have a line but a surface plane.
You can play around using the Manipulate command in Mathematica, so you can verify the change on the plane's position when coefficients a, b, & c change.

When the dependent variable is not in its simple (linear) form that indicates that x affects y in a proportional way, the relationship becomes non linear, i.e. non proportional.
This meas that either the variable x interrelates to itself, becoming x*x or x^2.
Then we have a second degree polynomial.

y = a + b x + c x^2

Manipulate[Plot[a + b x + c x^2 == 0, {x, -5, 5}],
{a, -20, 20}, {b, -10, 10}, {c, -50, 50}]

In a three dimensional form we may have a case that one variable affect the other.
Then we have the case

y = a + b x * c z => y = a + (bc) x*z

Manipulate[Plot3D[a + b x c y == 0, {x, -10, 10}, {y, -10, 10}],
{a, 0, 20}, {b, -5, 5}, {c, -5, 5}]

This implies that the surface bends. The opposite type of a bend we have whenever we have a division as:

y = a + ( b x / c z )

Manipulate[Plot3D[a + b x / c y == 0, {x, -10, 10}, {y, -10, 10}],
{a, 0, 20}, {b, -5, 5}, {c, -5, 5}]

The general case in the three dimensional relationship is:

y = a + b x + c x^2 + d x z + e z^2 + f z

Manipulate[Plot3D[a + b x + c x^2 + d x y + e y^2 + f y == 0, {x, -10, 10}, {y, -10, 10}], {a, -200, 200}, {b, -50, 50}, {c, -10, 10}, {d, -100, 100}, {e, -10, 10}, {f, -50 , 50}]

Manipulate[
Plot[a + b x + c x^2 + d x^3 == 0, {x, -1, 1}], {a, 0, 20}, {b, -10,
10}, {c, -5, 5}, {d, -20, 20}]

Manipulate[Plot[a + b x + c x^2 + d x^3 + e x^4 == 0, {x, -1, 10}],
{a, 0, 20}, {b, -10, 10}, {c, -5, 5}, {d, -20, 20}, {e, -3, 3}]

Then you can practice to see the planes defined on page 19 using:

Plot3D[3 x + 4 y == 18, {x, -10, 10}, {y, -20, 20}]

and

Plot3D[9 x + y == 21, {x, -10, 10}, {y, -20, 20}]

Then you can solve the system of these two equations by:

Solve[{3 x + 4 y == 18, 9 x + y == 21}, {x, y}]

and have its solution.

{{x -> 2, y -> 3}}

Finally, you can control the relationships on page 39 as:

Manipulate[Plot[a x ^b == 0, {x, -1, 1}], {a, -20, 20}, {b, -6, 6}]

on page 41:

Manipulate[Plot[a + b x , {x, 0, 10}], {a, 0, 20}, {b, 0, .99}]

Manipulate[Plot[a * x^b , {x, 0, 10}], {a, 0, 20}, {b, 0, .99}]

Manipulate[Plot[a * E^(-b x) , {x, 0, 10}], {a, 0, 20}, {b, 0, .99}]

Manipulate[Plot[a * (1 - E^(-b x)) , {x, 0, 10}], {a, 0, 20}, {b, 0, .99}]

Manipulate[Plot[a x ^b == 0, {x, 0, 10}], {a, 0, 20}, {b, 1, 5}]

Manipulate[Plot[a x ^b == 0, {x, 0, 10}], {a, 0, 20}, {b, -6, .99}]


Finally, if you want to indicate an influence diagram yoou may use:

LayeredGraphPlot[{"Price" -> "Revenue", "Revenue" -> "Profit",
"Advertising" -> "Units Sold", "Advertising" -> "Cost",
"Units Sold" -> "Revenue", "Seasonal Factors" -> "Units Sold",
"Unit Cost" -> "Cost of Goods", "Cost of Goods" -> "Cost",
"Sales Expence" -> "Cost", "Overhead" -> "Cost" ,
"Cost" -> "Profit"}, Left, VertexLabeling -> True]