Answer:
A strong positive correlation
Step-by-step explanation:
Since the dependent variable increases as the independent variable increases, this is a positive correlation.
Plotting these points, we can see that they form a nearly straight line. This makes it a strong correlation.
A strong positive correlation best describes the strength of the given model. So, option B is correct.
The correlation coefficient is used to measure the strong relationship between the two variables.
The formula for the correlation coefficient
[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]
We need to calculate the correlation coefficient and then make a conclusion about its value.
Form a table as shown where x is the cost of items and y is the shipping cost. The table becomes
x y XY x² y²
25 5.99 149.8 625 35.9
45 8.99 404.6 2025 80.8
50 8.99 449.5 2500 80.8
70 10.99 769.3 4900 120.8
190 34.96 1773.2 10050 318.3
The formula for the correlation coefficient
[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]
where n=4
[tex]= \frac{ 4(1773.2)-(190)(34.96)} {\sqrt{{[4(10050)-190^2] [4(318.3)-34.96^2]}} }[/tex]
r[tex]=\frac{450}{4100\times51}[/tex]
r = 450 / √209100
r = 450/457.3
r = 0.98409
Thus, The value of r indicates a stronger positive correlation.
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