Correlation: Meaning, Types, Methods and Interpretation Questions

Question 1

Define correlation.

Accepted Answer

Correlation is a statistical measure that shows the degree and direction of relationship between two variables.

Question 2

What is positive correlation?

Accepted Answer

Positive correlation means two variables move in the same direction (increase together or decrease together).

Question 3

What is negative correlation?

Accepted Answer

Negative correlation means two variables move in opposite directions (one increases while the other decreases).

Question 4

State the range of Pearson’s correlation coefficient (r).

Accepted Answer

Pearson’s correlation coefficient r lies between -1 and +1.

Question 5

What is a scatter diagram?

Accepted Answer

A scatter diagram is a graph of paired values (x, y) used to visually study correlation.

Question 6

Correlation does not imply what?

Accepted Answer

Correlation does not imply causation (cause-and-effect).

Question 7

Write any three types of correlation.

Accepted Answer

Types of correlation include:

1) Positive, negative and zero correlation (by direction).
2) Simple, multiple and partial correlation (by number of variables).
3) Linear and non-linear correlation (by form).

(Any three types can be written.)

Question 8

Explain correlation vs causation (any three points).

Accepted Answer

Correlation vs causation:

1) Correlation shows association; causation shows one variable causes change in another.
2) Correlation can exist due to a third factor (spurious correlation).
3) Correlation coefficient alone cannot establish cause-effect; further study is needed.

(Any three points can be written.)

Question 9

Explain scatter diagram method (any three points).

Accepted Answer

Scatter diagram method:

1) Plot each (x, y) pair as a point on a graph.
2) Upward pattern indicates positive correlation; downward indicates negative correlation.
3) Random scatter indicates no correlation; closeness of points shows strength.

(Any three points can be written.)

Question 10

Write any three properties of Pearson’s coefficient r.

Accepted Answer

Properties of Pearson’s r:

1) -1 ≤ r ≤ +1.
2) Sign (+/−) shows direction; magnitude shows strength.
3) r is not affected by change of origin and scale (unit change).

(Any three properties can be written.)

Question 11

Write any three uses of correlation in business.

Accepted Answer

Uses of correlation in business include:

1) Studying relationship between advertising and sales for planning.
2) Forecasting and estimating demand using related variables.
3) Supporting regression analysis and decision making.

(Any three uses can be written.)

Question 12

Mention any three limitations/precautions of correlation.

Accepted Answer

Limitations/precautions of correlation:

1) Correlation does not indicate causation.
2) Pearson’s r measures linear relationship only; r=0 may still have non-linear relation.
3) Extreme values and mixed data can mislead correlation results.

(Any three points can be written.)

Question 13

Explain correlation and its types with suitable examples and a table.

Accepted Answer

Correlation is a statistical measure of how two variables are related. It tells both the direction (positive/negative) and the degree (strength) of relationship between variables such as price and demand, income and consumption, advertising and sales.

Types of correlation:

| Type | Meaning | Example |
|---|---|---|
| Positive | variables move together | advertising and sales (generally) |
| Negative | move in opposite direction | price and demand |
| Zero | no linear relation | unrelated variables |
| Linear | points form straight-line pattern | income and expenditure (approx.) |
| Non-linear | relation is curved | learning and performance (may level off) |

Thus, correlation helps understand business relationships and supports forecasting and planning.

Question 14

Explain Pearson’s correlation coefficient and interpretation using a flowchart/table.

Accepted Answer

Karl Pearson’s coefficient of correlation (r) measures the strength and direction of linear relationship between two variables.

Important points:

- r lies between -1 and +1.
- r > 0: positive correlation; r < 0: negative correlation.
- |r| close to 1 indicates strong correlation; |r| close to 0 indicates weak correlation.

| r value (approx.) | Interpretation |
|---|---|
| 0 to ±0.25 | very weak |
| ±0.25 to ±0.50 | weak |
| ±0.50 to ±0.75 | moderate |
| ±0.75 to ±1.00 | strong |

```mermaid
flowchart LR
  A[Collect paired data (X,Y)] --> B[Compute r]
  B --> C[Check sign (+/−)]
  C --> D[Interpret direction]
  B --> E[Check magnitude |r|]
  E --> F[Interpret strength]
  F --> G[Use for decisions/forecast
(with caution)]
```

Therefore, Pearson’s r is very useful for measuring linear association, but it should be interpreted carefully because correlation does not prove causation.

Question 15

Write a detailed note on Spearman’s rank correlation and when it is used. Include formula and steps.

Accepted Answer

Spearman’s rank correlation (ρ) is used when data are given in ranks (ordinal data) or when exact measurements are not available. It measures the correlation between two ranked variables.

Formula:

ρ = 1 − [ 6Σd² / n(n² − 1) ]

where:
- n = number of pairs
- d = difference between ranks of each pair

Steps to compute Spearman’s ρ:

1) Rank X and Y values (if ranks are not given).
2) Find d = (Rank X − Rank Y) for each pair.
3) Square the differences to get d² and sum Σd².
4) Substitute in the formula to obtain ρ.

Interpretation is similar to Pearson’s r: ρ ranges from -1 to +1, where +1 indicates perfect agreement in ranks and -1 indicates perfect reverse ranking.

Thus, Spearman’s rank correlation is especially useful in business surveys (preference rankings), performance ratings and situations where only order is meaningful.

Correlation: Meaning, Types, Methods and Interpretation

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