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Regression, Correlation and Hypothesis Testing

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Question 77

A marine biologist measured the dissolved oxygen level, ddd mg/L, at various depths, hhh meters, in a specific estuary. Data from a random sample of 10 locations are summarized as follows:

∑h=155∑h2=2875∑d=62.4Sdd=18.2∑hd=884.2 \sum h = 155 \quad \sum h^2 = 2875 \quad \sum d = 62.4 \quad S_{dd} = 18.2 \quad \sum hd = 884.2 ∑h=155∑h2=2875∑d=62.4Sdd​=18.2∑hd=884.2
a.

Calculate the values of ShhS_{hh}Shh​ and ShdS_{hd}Shd​.

[3]
b.

Calculate, to 3 significant figures, the product moment correlation coefficient between hhh and ddd.

[2]
c.

The biologist also measured the water temperature, ttt °C, at the same 10 locations. The product moment correlation coefficient between hhh and ttt was found to be −0.915-0.915−0.915.

Describe, giving a reason, the nature of the correlation you would expect to find between temperature (ttt) and dissolved oxygen (ddd).

[2]

Regression, Correlation and Hypothesis Testing Questions

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