7.
50 leaves were clipped from a plant. Priya and Gautam separately measured the areas and
distances from the apical tip, of all the leaves. The students plotted their values on
separate graphs, with the y-axis showed the distance and the x-axis showed the leaf area.
After fitting these graphs to straight lines, they found the following:
Priya’s graph: Slope 0.8 correlation coefficient 0.99
Gautam’s graph: Slope 1.0 correlation coefficient 0.90
You are now provided the distance of a leaf from the apical tip of the same plant, and
asked to predict the area of the leaf using this information. Whose graph should you use?
a. Priya’s
b. Gautam’s
c. Either would be equally good
d. Neither, since the leaf area is the independent variable
Priya’s graph shows superior linear fit for predicting leaf area from distance due to its higher correlation coefficient. In plant physiology experiments like this JGEEBILS question, the correlation coefficient (r) measures prediction reliability more than slope alone. Select Priya’s graph (option a) for accurate leaf area estimation.
Question Analysis
50 leaves from one plant yield linear regressions: y-axis distance (cm), x-axis leaf area (cm²). Priya: slope=0.8, r=0.99; Gautam: slope=1.0, r=0.90. Task requires predicting area (y) from known distance (x).
Option Breakdown
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a. Priya’s: Correct. r=0.99 indicates 98% variance explained (r²=0.98), tight data scatter around line for reliable predictions.
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b. Gautam’s: Incorrect. r=0.90 (r²=0.81) shows more scatter, reducing prediction confidence despite steeper slope.
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c. Either equally good: Wrong. Higher r proves Priya’s superior fit; equal use ignores statistical strength.
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d. Neither, independent variable issue: Incorrect. Leaf area (x) manipulated, distance (y) response in experiment. Prediction reverses axes via regression equation y = slope × x + intercept.
Statistical Decision Factors
Correlation coefficient r quantifies linearity strength: |r| closer to 1 means better fit. Priya’s r=0.99 >> Gautam’s r=0.90 signals less measurement error or outliers in her data . Slope reflects biological allometry (area-distance scaling), but poor r invalidates Gautam’s for CSIR NET-level prediction .
Plant Biology Context
Leaf area increases with distance from apical meristem due to expansion post-primordia formation. High r confirms strong allometric relationship, common in shoot phyllotaxis studies. For JGEEBILS/CSIR NET, prioritize r over slope in regression choice.
