A group of researchers is interested in optimizing the extraction process that r

Question

A group of researchers is interested in optimizing the extraction process that removes spearmint oil from spearmint leaves (Mentha spicata L.). The group is trying to test their hypothesis that they will be able to extract more spearmint oil from denser leaves. The researchers weighed their leaves in mg (n=50 leaves), extracted oil from each leaf, and measured the amount of oil produced from each leaf in mL. Unfortunately, the vapors produced during spearmint oil extraction can be extremely irritating to the eye, so all of the researchers are currently taking a break from their work. Fortunately, they left their dataset in YOUR care!

1. What kind of a relationship do you expect to find between spearmint leaf mass and spearmint oil production?

2. For this study, which variable is the response variable (e.g. what is being effected?)? Which variable is the predictor variable (e.g. what is affecting the response?)? Response variable:

Predictor variable:

3. Test your predicted relationship from question #1 given the data provided in the Excel spreadsheet. Plot the data and run the appropriate statistical analysis. Interpret your data and then provide a brief written analysis. Do your results agree with your prediction(s) in question #1?

Leaf mass (mg) Spearmint Oil (mL) 6 4 17 2 6 7 11 7 13 3 15 7 14 5 7 2 21 2 13 7 11 6 8 1 18 2 24 2 23 6 6 5 14 3 15 3 19 2 10 6 24 3 21 1 11 4 23 1 23 3 22 5 19 5 6 3 10 4 8 6 21 3 19 1 20 5 8 5 14 2 14 7 14 6 9 5 5 7 25 3 20 3 18 3 10 2 11 3 9 1 14 7 23 2 18 5 23 5 12 4

Explanation / Answer

1)

Based on the data we can see that correlation (r) is 0.30. Hence there is a mild positive correlation between the two. It means that as value of one variable goes up, the other goes up as well.

2)

Spearmint Oil (mL) is the response variable whereas Leaf mass (mg) is the predictor variable.

3)

Spearmint Oil (mL)=5.39-0.0987(Leaf mass (mg)) is the equation. We can see that the p-value is less than 0.05 for intercept and slope. Hence, test is significant.

SUMMARY OUTPUT Regression Statistics Multiple R 0.303489 R Square 0.092105 Adjusted R Square 0.073191 Standard Error 1.863923 Observations 50 ANOVA df SS MS F Significance F Regression 1 16.91792 16.91792 4.869572 0.032151 Residual 48 166.7621 3.47421 Total 49 183.68 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5.390694 0.7167 7.521549 0.00 3.949672 6.831716 Leaf mass (mg) -0.0987 0.044729 -2.20671 0.03 -0.18864 -0.00877

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