Question

Based on the ordered pairs in the data below, state whether there is no correlation, a weak correlation, or strong correlation . If there is indeed correlation, determine whether the correlation is negative or positive.

X: 1, 2, 3, 4, 5, 6, 7, 8, 9,
Y: 2, 3, 8, 10, 26, 38, 46, 50, 68

The data above has
A. No correlation
B. A weak correlation
C. A strong correlation

The data above has:
A. No correlation
B. A negative correlation
C. A positive correlation

Answer 1

The data above has:

C. A strong correlation

The data above has:

C. A positive correlation

Explanation:

We have a ordered pairs in the data as:

x y

1 2

2 3

3 8

4 10

5 26

6 38

7 46

8 50

9 68

Clearly on plotting the scatter plot on the basis of table of values we see that the relation is a strong correlation since we can find a relationship between variable x and y.

i.e. the points will lie above or below the curve which is formed by connecting some points of the scatter plot and are not scattered away.

Hence, the data above has a:

C. A strong correlation.

Also the graph is a positive correlation since with the increasing value of x the y-value also increases.

Answer 2

• C. strong correlation
• C. positive correlation

Explanation:

The correlation coefficient for two sets of data is the ratio of their covariance to the product of their standard deviations. The magnitude of this ratio will be high when there is a fairly predictable relationship between the data in one of the data sets and the data in the other. When plotted on a graph, the two sets of data will have the highest correlation when the graph best approximates a straight line.

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graph

Attached is a graph of the data, along with a calculation of the correlation coefficient: r ≈ 0.9756. We notice that the data is reasonably well predicted by the "line of best fit" shown on the graph along with the data.

correlation strength

The fact that the magnitude of the correlation coefficient is near 1 indicates a "strong" correlation. The value required for categorization as "strong" or "weak" correlation depends on the field. Technology fields generally require a higher value for "strong" correlation than some others (0.75 vs 0.6, for example).

Here, the correlation coefficient has a magnitude near 0.98, so the data is considered to have a strong correlation.

correlation sign

The correlation coefficient will have a positive sign if increasing "inputs" are generally associated with increasing "outputs." If increasing inputs are associated with decreasing outputs, then the correlation coefficient will be negative.

Here, the sign of the correlation coefficient indicates a positive correlation. The graph confirms that increasing x-values are associated with increasing y-values.