Linear Regression Interview Question| Does high linear correlation coefficient imply linear relationship ?
Question
Refer to the following table to answer the question :
| City | Temperature(in °C) | Sales of Laptops(in thousands) |
| Kanpur | 18 | 100 |
| Benaras | 19 | 121 |
| Patna | 19 | 144 |
| Indore | 23 | 189 |
| Kolkata | 24 | 200 |
| Bangalore | 25 | 254 |
| Mumbai | 27 | 268 |
| Chennai | 29 | 280 |
The Pearson linear correlation coefficient between Temperature of cities and the Sales of laptop in those cities is 0.97. So can we conclude that if the temperature increases in these cities then laptop sales also increase linearly ?
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Answer ( 1 )
A high linear correlation coefficient between Temperature of cities and Sales of Laptops in those cities does not necessarily imply a causal relationship between them. Such correlations are called spurious correlations. There might be multiple unknown factors that affect the sales of laptops in those cities and temperature has no causal effect on these sales. Such correlations are misleading .