Input:

The year list contains the periods of the year represented as a decimal number year+month/12. The sales list contains the sales in thousands of USD for the corresponding periods in the year list. We will use linear regression to find the trend line. From the initial graph, we notice that the trend is linear in nature.

# source_code/6/sales_year.r
#Predicting sales based on the period in the year
sales = data.frame(
    year = c(2010.000000, 2010.083333, 2010.166667, 2010.250000,
             2010.333333, 2010.416667, 2010.500000, 2010.583333,
             2010.666667, 2010.750000, 2010.833333, 2010.916667,
             2011.000000, 2011.083333, 2011.166667, 2011.250000,
             2011.333333, 2011.416667, 2011.500000, 2011.583333,
             2011.666667, 2011.750000, 2011.833333, 2011.916667,
             2012.000000, 2012.083333, 2012.166667, 2012.250000,
             2012.333333, 2012.416667, 2012.500000, 2012.583333,
             2012.666667, 2012.750000, 2012.833333, 2012.916667,
             2013.000000, 2013.083333, 2013.166667, 2013.250000,
             2013.333333, 2013.416667, 2013.500000, 2013.583333,
             2013.666667, 2013.750000, 2013.833333, 2013.916667,
             2014.000000, 2014.083333, 2014.166667, 2014.250000,
             2014.333333, 2014.416667, 2014.500000, 2014.583333,
             2014.666667, 2014.750000, 2014.833333, 2014.916667,
             2015.000000, 2015.083333, 2015.166667, 2015.250000,
             2015.333333, 2015.416667, 2015.500000, 2015.583333,
             2015.666667, 2015.750000, 2015.833333, 2015.916667,
             2016.000000, 2016.083333, 2016.166667, 2016.250000,
             2016.333333, 2016.416667, 2016.500000, 2016.583333,
             2016.666667, 2016.750000, 2016.833333, 2016.916667,
             2017.000000, 2017.083333, 2017.166667, 2017.250000,
             2017.333333, 2017.416667, 2017.500000, 2017.583333,
             2017.666667, 2017.750000, 2017.833333, 2017.916667),
    sale = c(10.500000, 11.900000, 13.400000, 12.700000, 13.900000,
             14.000000, 13.500000, 14.500000, 14.300000, 14.900000,
             16.900000, 17.400000, 11.900000, 12.600000, 13.500000,
             13.600000, 14.600000, 14.400000, 15.700000, 14.000000,
             15.500000, 15.800000, 16.500000, 20.100000, 13.200000,
             14.400000, 16.100000, 14.900000, 15.700000, 15.300000,
             16.800000, 15.700000, 16.800000, 16.300000, 18.700000,
             19.700000, 14.600000, 15.400000, 16.200000, 17.800000, 
             17.800000, 16.100000, 17.400000, 17.000000, 17.200000,
             17.900000, 20.500000, 22.500000, 15.100000, 17.400000,
             17.200000, 17.800000, 18.600000, 18.900000, 18.300000,
             17.900000, 19.200000, 18.800000, 20.400000, 23.000000,
             16.500000, 17.900000, 19.600000, 20.200000, 19.100000,
             19.700000, 19.700000, 20.500000, 20.300000, 20.300000, 
             22.400000, 23.800000, 18.900000, 19.500000, 19.800000,
             19.700000, 20.800000, 21.100000, 21.000000, 21.000000,
             20.600000, 21.400000, 23.700000, 24.600000, 20.000000,
             20.800000, 22.100000, 20.900000, 21.500000, 22.100000,
             22.600000, 22.700000, 21.900000, 22.900000, 24.000000,
             26.600000)
)

model = lm(sale ~ year, data = sales)
print(model)

Output:

$ Rscript sales_year.r
Call:
lm(formula = sale ~ year, data = sales)
Coefficients: (Intercept)      year
                -2557.778     1.279

Therefore, the equation of the trend line is:

sales = 1.279*year-2557.778

Visualization:

Now we add the trend line to the graph: