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Regression, Correlation and Hypothesis Testing

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Question 71

A biologist studying bacterial growth records the incubation time, ttt minutes, and the mass of nutrients consumed, mmm milligrams, for n=15n = 15n=15 separate samples. Each sample is initially provided with a petri dish containing 18.018.018.0 mg of nutrient. The summary statistics for these 151515 samples are as follows:

∑t=202.5,∑m=49.5,∑tm=745.2,Stt=1440.0,Smm=7.5 \sum t = 202.5, \quad \sum m = 49.5, \quad \sum tm = 745.2, \quad S_{tt} = 1440.0, \quad S_{mm} = 7.5 ∑t=202.5,∑m=49.5,∑tm=745.2,Stt​=1440.0,Smm​=7.5
a.

Calculate the product moment correlation coefficient between ttt and mmm.

[3]
b.

The mass of nutrient remaining in the dish at the end of the incubation period is recorded as RRR milligrams. (i) Write down an equation for RRR in terms of mmm. (ii) State the value of the product moment correlation coefficient between RRR and mmm.

[2]
c.

State the value of the product moment correlation coefficient between ttt and RRR.

[1]

Regression, Correlation and Hypothesis Testing Questions

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