14.25 Plant Emissions. Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses. N. Agelopolous et al. examined factors that affect the emission of volatile compounds by the potato plant Solanum tuberosum and published their findings in the paper "Factors Affecting Volatile Emissions of Intact Potato Plants, Solanum tuberosum: Variability of Quantities and Stability of Ratios" (Journal of Chemical Ecology, Vol. 26(2), pp. 497-511). The volatile compounds analyzed were hydrocarbons used by other plants and animals. Following are data on plant weight $\left(x\right)$, in grams, and quantity of volatile compounds emitted $\left(y\right)$, in hundreds of nanograms, for 11 potato plants.

Step by step solution

01

Given Information

Given table:

For regression by the variables under investigation, find the meeting assumptions 1-3.

02

Explanation

Regression-inference Assumptions 1-3 must be met if there are constants ${\beta }_0,{\beta }_1$and $\sigma$such that the amounts of volatile chemicals emitted by all potato plants of that weight have a normal distribution with mean ${\beta }_0+{\beta }_1$and standard deviation $\sigma$for a given weight, $x.$.

Graphical representation:

The assumptions for regression inferences are visually displayed in the picture above, and they appear to be met.

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