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Which best describes the strength of the model?
The table shows the shipping costs for items of different
values.
Shipping Costs for Items
Total cost of items Shipping costs
$25
$5.99
$45
$8.99
$50
$8.99
$70
$10.99
a weak positive correlation
a strong positive correlation
a weak negative correlation
a strong negative correlation
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Answer:

A strong positive correlation.

Step-by-step explanation:

The question requires you to calculate the correlation coefficient and then make a conclusion about its value.

Form a table as shown where x is cost of items and y is shipping cost

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 ------sum

The formula for correlation coefficient follows;

r=n(∑xy)-(∑x)(∑y) ÷ √{[n∑x²-(x)²] [n∑y²-(y)²]}

where n=4

r=4(1773.2)-(190)(34.96) ÷ √{[4(10050)-190²] [4(318.3)-34.96²]}

r=450÷ √{4100*51)

r=450÷√209100

r=450÷457.3

r=0.98409

The value of r indicates a stronger positive correlation

Step-by-step explanation:

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