Question

1. The following data are claims (in $millions) for Blue cross Blue shield benefits benefits for nine states, along with the surplus (in $millions) that the company had in assets in those states.

State                  Claims          Surplus

Alabama               1425              277

Colorado                 273              100

Florida                   915             120

Illinois                  1687              259

Maine                     234                40

Montana                 142                25

North Dakota          259               57

Oklahoma               258               31

Texas                       894             141

Use the data to compute a correlation coefficient, to determine the correlation   between claims and surplus. Interpret the results accordingly explain all variables under study along with their significance. Further explain entire concept of Correlation using 5 real life situations which explains the concept of correlation in detail. Make use of appropriate reference and enrich your literature review appropriately

Answer 1

Let X : Claims

And Y : surplus

The following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	1425	277	394725	2030625	76729
	273	100	27300	74529	10000
	915	120	109800	837225	14400
	1687	259	436933	2845969	67081
	234	40	9360	54756	1600
	142	25	3550	20164	625
	259	57	14763	67081	3249
	258	31	7998	66564	961
	894	141	126054	799236	19881
Sum =	6087	1050	1130483	6796149	194526

The correlation coefficient rr is computed using the following expression:

where

In this case, based on the data provided, we get that,

Therefore, based on this information, the sample correlation coefficient is computed as follows

Which indicates that there is a high degree correlation between the claims and surplus.

Following are the properties of correlation coefficient:

1. Limit: Coefficient values can range from +1 to -1, where +1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and a 0 indicates no relationship exists..
2. Pure number: It is independent of the unit of measurement. For example, if one variable’s unit of measurement is in inches and the second variable is in quintals, even then, Pearson’s correlation coefficient value does not change.
3. Symmetric: Correlation of the coefficient between two variables is symmetric. This means between X and Y or Y and X, the coefficient value of will remain the same.

Degree of correlation:

1. Perfect: If the value is near ± 1, then it said to be a perfect correlation: as one variable increases, the other variable tends to also increase (if positive) or decrease (if negative).
2. High degree: If the coefficient value lies between ± 0.50 and ± 1, then it is said to be a strong correlation.
3. Moderate degree: If the value lies between ± 0.30 and ± 0.49, then it is said to be a medium correlation.
4. Low degree: When the value lies below + .29, then it is said to be a small correlation.
5. No correlation: When the value is zero.

Positive Correlation

A positive correlation is a relationship between two variables where if one variable increases, the other one also increases. A positive correlation also exists in one decreases and the other also decreases.

Examples of Positive Correlations

• The more time you spend running on a treadmill, the more calories you will burn.

• Taller people have larger shoe sizes and shorter people have smaller shoe sizes.

• The longer your hair grows, the more shampoo you will need.

• The less time I spend marketing my business, the fewer new customers I will have.

• The more hours you spend in direct sunlight, the more severe your sunburn.

• The more money she saves, the more financially secure she feels.

• As the temperature goes up, ice cream sales also go up.

A negative correlation means that there is an inverse relationship between two variables - when one variable decreases, the other increases. The vice versa is a negative correlation too, in which one variable increases and the other decreases. These correlations are studied in statistics as a means of determining the relationship between two variables.

Common Examples of Negative Correlation

• A student who has many absences has a decrease in grades.

• As weather gets colder, air conditioning costs decrease.

• If a train increases speed, the length of time to get to the final point decreases.

• If a chicken increases in age, the amount of eggs it produces decreases.

No correlation examples:

For example, the relationship between intelligence quotient and weight of a person.

In that case correlation coefficient is zero.