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R Programming Assignment Help
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R Programming Assignment Illustrations and Solutions
Question :
The file ”density.csv” contains data from a growth experiment with blue-green algae.
In the experiment, CO2 is bubbled through the culture during 14 consecutive days.
Two replicates were considered for this experiment, each one corresponding to a mea-
surement (in log-scale) of the increased absorbance of light of a solution containing the
algae, which is typically interpreted as a measure of algae density.
Solution :
(a) Construct a scatter-plot (including the regression line) for log-density vs day.
Do the plots suggest a linear relationship between these variables? Explain.

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The scatter plot for day and the corresponding log density is constructed using R-code and
that the linear fit line is also super imposed on the same (Figure 1).
Figure 1: Scatter plot of days and log_density with linear fit
From Figure 1, it is seen that the points roughly travel in linear path from the bottom left to
top right corner of the figure, indicating an approximate linear relationship between the two
variables. However, the points deviate from the fitted line in a systematic curvilinear
pattern, suggesting a higher degree polynomial fit to be a better one.

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(b) Use the R-function cor(x,y) to obtain the correlation between the variables log-
density and day. Comment on this value.
The cov( ) function in R is used find the linear correlation coefficient between days and
log_density and its value is produced as R output below.
The correlation between days and log_density is found to be 0.97895 that is considerably
close to ‘1’, the upper limit for the correlation coefficient (-1 ≤ ρ ≤ +1). This indicates that
the variables days and log_density have a high positive association, implying that as the

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value of the one increases, the value of the other also increases. This, high value also
supports the view that there is good linear relationship between the two variables.

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