A company that manufactures solar energy systems performs a study on the relationship between average power obtained fro

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A company that manufactures solar energy systems performs a
study on the relationship between average power obtained from a
specific solar panel (X1, in kilowatt [kW]) and average daily
rainfall (X2, in mm). A sample of 30 solar panels is placed in
different geographical locations and, after a few weeks, the
average power obtained by each solar panel is registered. Parallel
measures of average daily rainfall for those exact same locations
are obtained:
X1. Average power [kW]
X2. Average daily rainfall [mm]
1.65 0.69
1.19 17.47
0.85 24.43
0.89 27.13
1.15 25.77
1.43 7.53
1.74 6.74
1.52 1.54
1.51 14.50
1.39 6.34
1.84 2.58
1.33 17.07
0.65 31.97
1.13 13.68
1.58 11.92
1.62 7.50
0.92 31.33
1.81 1.37
1.80 6.32
1.65 2.58
1.69 1.89
1.06 27.57
1.56 0.87
1.41 11.74
1.92 1.56
1.36 5.88
1.29 14.73
1.27 13.58
1.50 3.33
1.60 3.50
a) Compute the correlation between the two
variables. (5 points)
b) In your opinion, which of the two variables
(X1 and X2) should be considered as the independent or
explanatory variable in this case? Justify your answer. (5
points)
c) Based on your answer to the previous question, determine
the coefficients of the linear regression model. Write down the
complete linear regression model. (5 points)
d) Compute the coefficient of determination
(r2 or R squared) of this model. What would the
value of the coefficient of determination be if the variables in
the regression model were inverted – (independent or
explanatory variable (X) becomes Y, and dependent or
response variable (Y) becomes X)? Justify. (5 points)
e) Predict the value of X2 for a solar panel that
produces an average of 0.8 kW, using the linear model you’ve
determined in (c).
Predict the value of X1 for a panel installed in a
location with an average daily rainfall of 20 mm, using the linear
model you’ve determine in (c). (5 points)
f) Obtain an appropriate graphical representation of the
linear regression model. (note: in addition to the original graph,
please include or paste the graph as a picture to avoid any
formatting or conversion issue). (5 points).