Science:Math Exam Resources/Courses/MATH102/December 2019/Question 04 (a)

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MATH102 December 2019

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Question 04 (a)

Remember our fishy friends? The quality of hatching of larvae of cold-water fish depends on the temperature of the water. Each hatch is given a quality ranking from 0 to 10, with 10 being a perfect hatch. In different places along one particular stream, hatch quality and temperature was measured for two species, Northern Rock Sole and Southern Rock Sole. This data is graphed as points below. Also graphed is a fitted function. MATH 102 December 2019 Q4a In terms of sum of squared residuals, which of the two species of fish does the curve fit best? As always, justify your answer.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall that the SSR (sum of squared residuals) is given by $\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2},$ where $n$ is the number of data values, $y_{i}$ is the $i$th data value, and ${\hat {y}}_{i}$ is the estimate of the $i$th data value.

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Solution
The SSR (sum of squared residuals) for the NRS (Northern Rock Sole) is $(9-9)^{2}+(10-10)^{2}+(8-9)^{2}=1.$ The SSR (sum of squared residuals) for the SRS (Southern Rock Sole) is $(8.5-9)^{2}+(9.5-10)^{2}+(9-9)^{2}=0.5.$ Hence, the curve fits the SRS best.

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