Linear relationship
Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 6 "Correlation"
Meaning
A linear relationship is a link between two variables that a straight line can show. When one variable changes by a fixed amount, the other changes by a steady amount in response. This matters because Karl Pearson's coefficient of correlation (r) measures only linear relationships. If the link is curved, r can be close to zero even when the two variables are closely tied. A scatter diagram (a graph plotting each pair of values as a dot) shows whether the pattern is a straight line or a curve.
Example
In NCERT, X takes the values −3 to 3 and Y = X². Y depends fully on X, yet r = 0. The points form a U-shaped curve, not a line, so r finds no linear relation.
Don't confuse with
- Independence: r = 0 means only that there is no straight-line relation. The variables may still be linked in a non-linear way.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class