The correlation of the values in the tables is the existence of a
relationship between the x and y values.
Correct response:
Method used for the evaluation of the tables
A table that shows a strong correlation is one in which the y-values can be predicted more or less accurately from the x-values.
The table that shows no correlation is one in which the x and y-values have different patterns;
The level of correlation is given by the correlation coefficient, which is found by the following formula;
[tex]\displaystyle r = \mathbf{ \dfrac{\sum \left(x_i - \overline{x} \right) \cdot \left(y_i - \overline{y} \right)}{\sqrt{\sum \left(x_i - \overline{x} \right)^2 \cdot \sum \left(y_i - \overline{y} \right)^2} }}[/tex]
By plotting the values using MS Excel, we have the values of r², for the tables as follows;
The value of r² for the first table is r² = 0.7307
Therefore;
r ≈ 0.8548 The correlation of the first table is strong.
Second table, r² = 0.8156
r = √(0.8156) ≈ 0.9031 The correlation in the second table is very strong.
Third table, r² = 0.0107
Therefore, r ≈ 0.1034
- The correlation for the third table is weak, which shows no correlation.
Fourth table, r² = 0.9342
Therefore, r ≈ 0.9665
The correlation of the x and y-values of the fourth table is very strong indicating the presence of a correlation.
Therefore;
- The table that shows no correlation is the third table.
Learn more about correlation analysis here:
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