Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
5. Analyzing Lines of Fit
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Exercise 30 Page 208

Create a graph with one point for each day of the week and with Beach 1 and Beach 2 on the x- and y-axes, respectively.

Example Graph:

Answer: There is a positive correlation but not a causal relationship.
Reasoning: See solution.

Practice makes perfect

The scatter plot below depicts the attendance numbers at the local beaches of two separate towns for one consecutive week. Both beaches had relatively low attendance Monday through Friday, most likely because those are working days. On Saturday, the weather was beautiful and both beaches were very busy. On Sunday, the weather was great but only Beach 1 was open.

Is There a Correlation?

The correlation is positive and, other than the Sunday point (19,0), very strong. Possible correlation coefficients could range from between 0.7

Is the Relationship Causal?

Whether or not this is a causal relationship depends on quite a few factors, the main ones being:

  1. How close are the towns? If they are very close, residents of one town may travel to the beach of the other town occasionally. If they are far away, this may not be as possible.
  2. Are the beaches private for citizens of that particular town? If so, the residents of the other town would not be allowed to go to the other beach.

More than likely, the biggest factors of the attendance numbers for both beaches would be weather and day of the week. The attendance of Beach 1 does not directly influence the attendance of Beach 2, outside factors do. Therefore, it is not a causal relationship.