S1 MBA

STATISTICS FOR MANAGEMENT TOPIC-CORRELATION

DEFINITIONS  Correlation deals with the association with two more variables. [variable is any entity that can take on different values. For instance, age can be considered a variable because age can take different values for different people or for the same person at different times]  An analysis of co -variation between two or more variables  An attempt to determine degree of relationship.

Difference between correlation and causal relationship Correlation gives degree of relationship Causal relationship shows a relation

STEPS INVOLVED 1. Determine whether a relation exists. 2. Test to know whether it is significant. 3. Establish the cause and effect relation.

TYPES OF CORRELATION 1. POSITIVE CORRELATION 2. NEGATIVE CORRELATION 3. SIMPLE CORRELATION 4. MULTIPLE CORRELATION 5. PARTIAL CORRELATION 6. LINEAR CORRELATION 7. NON-LINEAR CORRELATION

POSITIVE CORRELATION When two variables move in the same direction then the correlation between these two variables is said to be Positive Correlation. ie or

POSITIVE CORRELATION GRAPH MODEL

EXAMPLE In the summer as the temperature increases people are thirstier. Temperature (F) Water Consumption (ounces)

NEGATIVE CORRELATION In this type of correlation, the two variables move in the opposite direction. When the value of a variable increases, the value of the other variable decreases.

NEGATIVE CORRELATION GRAPH MODEL

EXAMPLE Demand increases when price decreases. Price (Rs)Demand (MT)

SIMPLE CORRELATION In simple correlation we study only two variables

MULTIPLE CORRELATION When three or more variables are studied simultaneously.

PARTIAL CORRELATION In partial correlation though more than two factors are involved but correlation is studied only between two factors and the other factors are assumed to be constant.

LINEAR CORRELATION Linear correlation The amount of change in one variable tends to bear constant ratio to the amount of change in other variable Eg : X – 10, 20, 30, 40, 50. Y- 70, 140, 210, 280, 350.

NON- LINEAR CORRELATION The amount of change in one variable doesn't bear constant ratio to the amount of change in other variable. Eg: X – 100, 120, 370, 600. Y- 70, 110, 675, 1045

METHODS OF STUDYING CORRELATION 1. Karl Pearson’s coefficient of correlation. 2. Rank correlation coefficient. 3. Concurrent Deviation Method. 4. Method of Least Squares. 5. Scattered Diagram Method 6. Graphic Method.

Karl Pearson’s Method a. Direct Method b. Short cut Method c. Assumed Mean Method

Direct method Correlation Co-efficient : Correlation(r) =[ nΣXY - (ΣX)(ΣY) / Sqrt([nΣX 2 - (ΣX) 2 ][nΣY 2 - (ΣY) 2 ])] n = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX 2 = Sum of square First Scores ΣY 2 = Sum of square Second Scores

Assumed mean method Correlation(r) =[ nΣdxdy - (Σdx)(Σdy) / Sqrt([nΣdx 2 - (Σdx) 2 ][nΣdy 2 - (Σdy) 2 ])] n = Number of values or elements dx=given X value-assumed value dy=given Y value-assumed value

Short cut method Correlation(r) =Σxy / Sqrt([Σx 2 *Σy 2 )]

STRENGTH & DIRECTION

ADVANTAGES OF KARL PEARSON’S CORRELATION Gives relationship between variables. Proves type of relation

DISADVANTAGES OF KARL PEARSON’S CORRELATION It cannot prove an actual cause and effect connection

LEAD & LAG IN CORRELATION The time gap before a cause and effect relationship is established is called Lag. Eg: Increased Supply of commodity may not have immediate effect on price

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