Question

coffee shop sales
maurice and beatrice opened a new store called the trendy café. their goal is to reach a profit of $25,000 in their 30th month of business. the table and scatter - plot below represent the profit in thousands of dollars, p, that they made during the first 12 months.
the trendy café profits
months, t: 1 2 3 4 5 6 7 8 9 10 11 12
profit in thousands of dollars, p: 3.5 3.0 4.0 5.5 7.0 6.5 7.5 7.0 7.5 8.0 9.0 8.5

1. what type of correlation/association do you notice in the data? is the correlation strong or weak?
2. does this relationship show causation? explain.
3. a line is graphed along with the data. is this an appropriate trend line for the data? why or why not?

Explanation:

Step1: Analyze correlation type

As the number of months increases, the profit generally increases, so it is a positive correlation.

Step2: Determine correlation strength

The data points are somewhat scattered around the potential trend - line, so the correlation is weak.

Step3: Consider causation

Just because profit increases with months doesn't mean months cause profit. There could be other factors like marketing efforts, seasonality etc. So, no causation.

Step4: Evaluate trend - line

The line seems to pass through the general area of the data points and captures the overall upward trend, so it is an appropriate trend - line.

Answer:

1. Positive correlation; weak
2. No. Other factors may affect profit.
3. Yes. It represents the overall trend.