(Solved Homework): Locate the results of a recent survey that shows at least two variables in a newspaper,…

Locate the results of a recent survey that shows at least two variables in a newspaper, magazine, or internet article. Outline the survey data so that your peers can understand the variables and results, and then identify at least one key formula from this module that you could use to evaluate the data. Provide a brief explanation of why you selected the formula you did and why it matters.

Expert Answer

Survey: Number of ice cream sold by a local ice cream shop versus the temperature on that day for 12 days.
Ice Cream Sales vs Temperature

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Temperature °C Ice Cream Sales
(Y) (X)
14.2° $215

16.4° $325

11.9° $185

15.2° $332

18.5° $406

22.1° $522

19.4° $412

25.1° $614

23.4° $544

18.1° $421

22.6° $445

17.2° $408

Below is the scatter plot of the above data:

As we can see the data is following somewhat linear curve, we can use correlation/simple linear regression as our
evaluation method.
The correlation can be calculated using the formula –

From the above data we get –

$sum xy = 95506.6$ , $sum x = 4829$ , $sum Y = 224.1$ , $sum X^{2} = 2118025$ $and sum Y^{2} = 4362.05$

So, the correlation will be –

$r = frac{95506.6-frac{4829 times 224.1}{12}}{sqrt{[2118025-frac{(4829)^{2}}{12}][4362.05-frac{(224.1)^{2}}{12}]}}$

So, r = 0.9575.

This shows a very high linear relationship between the two variables.

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