Correlation of linear functions is used in determining different types of relationships that exists within the aforementioned functions. Relations created can be either direct or indirect as in the case below:
From the table above, the solid line creates a correlation between purchase of TVs and Refrigerators which assists in predicting changes depicted while purchasing either of the variables. These variables are based on such factors as income, education, preference and temperatures. In this case, people who lack television sets (0) possess the highest number of refrigerators (110). Thus, it is assumedly clear that there exists an indirect relationship between TV and refrigerators purchases which is created by the parallel line inequality.
While interpreting the graph from its left to right, a dashed line can be used to depict a decreasing function which is noted as: Y=XT. Whereby, (T) represents the gradient constant or the average rate of change between numbers of refrigerators while (x) represents the number of televisions (y) purchased. For instance, the coordinates T =y (0, 330) -x (110, 0), derives T= -3.3 and the equation transforms to x=-3.3y
|
Subject |
Number of Refrigerators (X) |
Number of TVs (Y) |
XY |
X2 |
Y2 |
|
1. |
110 |
0 |
0 |
12100 |
0 |
|
2. |
0 |
330 |
0 |
0 |
108900 |
|
Total (∑ ) |
110 |
330 |
36300 |
12100 |
108900 |
Formula for calculation of correlation coefficient is given as:
Whereby, N(sample size) = 2 and R= -2.75 * 10-0.05 (negative sign indicates a negative direction and not the strength of coefficiency).
The correlation derived helps in predicting future purchases of television sets in respect to refrigerators. Thus, it is recommended that both electronic manufacturers and sales men improve their advertisement of refrigerators to consumers as well as lower their respective market prices. However, the major disadvantage attributed to this correlation is the fact that it fails to measure the real cause behind negative correlations. Also, the fact that television and refrigerators variables are in one way or another related does not necessary postulate that one is the cause while the other the result.
All, in all, it is fair to indicate that there exists an indirect correlation that expounds on the decrease in purchase of either of the two variables.