This function considers linear relationships between two pollutants. The relationships are calculated on different times bases using a linear model. The slope and 95 in slope relationships by time unit are plotted in many ways. The function is particularly useful when considering whether relationships are consistent with emissions inventories.

## Usage

```
linearRelation(
mydata,
x = "nox",
y = "no2",
period = "month",
condition = FALSE,
n = 20,
rsq.thresh = 0,
ylab = paste0("slope from ", y, " = m.", x, " + c"),
auto.text = TRUE,
cols = "grey30",
date.breaks = 5,
...
)
```

## Arguments

- mydata
A data frame minimally containing

`date`

and two pollutants.- x
First pollutant that when plotted would appear on the x-axis of a relationship e.g.

`x = "nox"`

.- y
Second pollutant that when plotted would appear on the y-axis of a relationship e.g.

`y = "pm10"`

.- period
A range of different time periods can be analysed. The default is

`month`

but can be`year`

and`week`

. For increased flexibility an integer can be used e.g. for 3-month values`period = "3 month"`

. Other cases include`"hour"`

will show the diurnal relationship between`x`

and`y`

and “weekday” the day of the week relationship between`x`

and`y`

. “day.hour” will plot the relationship by weekday and hour of the day.- condition
For

`period = "hour"`

,`period = "day"`

and`period = "day.hour"`

, setting`condition = TRUE`

will plot the relationships split by year. This is useful for seeing how the relationships may be changing over time.- n
The minimum number of points to be sent to the linear model. Because there may only be a few points e.g. hours where two pollutants are available over one week,

`n`

can be set to ensure that at least`n`

points are sent to the linear model. If a period has hours <`n`

that period will be ignored.- rsq.thresh
The minimum correlation coefficient (R2) allowed. If the relationship between

`x`

and`y`

is not very good for a particular period, setting`rsq.thresh`

can help to remove those periods where the relationship is not strong. Any R2 values below`rsq.thresh`

will not be plotted.- ylab
y-axis title, specified by the user.

- auto.text
Either

`TRUE`

(default) or`FALSE`

. If`TRUE`

titles and axis labels will automatically try and format pollutant names and units properly e.g. by subscripting the ‘2’ in NO2.- cols
Colour for the points and uncertainty intervals.

- date.breaks
Number of major x-axis intervals to use. The function will try and choose a sensible number of dates/times as well as formatting the date/time appropriately to the range being considered. This does not always work as desired automatically. The user can therefore increase or decrease the number of intervals by adjusting the value of

`date.breaks`

up or down.- ...
Other graphical parameters. A useful one to remove the strip with the date range on at the top of the plot is to set

`strip = FALSE`

.

## Value

As well as generating the plot itself,

`linearRelation`

also returns an object of class
``openair''. The object includes three main components:

`call`

, the command used to generate the plot;

`data`

, the data frame of summarised information used to
make the plot; and `plot`

, the plot itself. If retained,
e.g. using ```
output <- linearRelation(mydata, "nox",
"no2")
```

, this output can be used to recover the data,
reproduce or rework the original plot or undertake further
analysis.

An openair output can be manipulated using a number of generic operations,
including `print`

, `plot`

and `summary`

.

## Details

The relationships between pollutants can yield some very useful
information about source emissions and how they change. A
scatterPlot between two pollutants is the usual way to investigate
the relationship. A linear regression is useful to test the
strength of the relationship. However, considerably more
information can be gleaned by considering different time periods,
such as how the relationship between two pollutants vary over
time, by day of the week, diurnally and so on. The
`linearRelation`

function does just that - it fits a linear
relationship between two pollutants over a wide range of time
periods determined by `period`

.

`linearRelation`

function is particularly useful if
background concentrations are first removed from roadside
concentrations, as the increment will relate more directly with
changes in emissions. In this respect, using `linearRelation`

can provide valuable information on how emissions may have changed
over time, by hour of the day etc. Using the function in this way
will require users to do some basic manipulation with their data
first.

If a data frame is supplied that contains `nox`

, `no2`

and `o3`

, the `y`

can be chosen as `y = "ox"`

. In
function will therefore consider total oxidant slope (sum of NO2 +
O3), which can provide valuable information on likely vehicle
primary NO emissions. Note, however, that most roadside sites do
not have ozone measurements and `calcFno2`

is the
alternative.

## Examples

```
# monthly relationship between NOx and SO2 - note rapid fall in
# ratio at the beginning of the series
linearRelation(mydata, x = "nox", y = "so2")
# monthly relationship between NOx and SO2 - note rapid fall in
# ratio at the beginning of the series
if (FALSE) linearRelation(mydata, x = "nox", y = "ox")
# diurnal oxidant slope by year # clear change in magnitude
# starting 2003, but the diurnal profile has also changed: the
# morning and evening peak hours are more important, presumably
# due to change in certain vehicle types
if (FALSE) linearRelation(mydata, x = "nox", y = "ox", period = "hour", condition = TRUE)
# PM2.5/PM10 ratio, but only plot where monthly R2 >= 0.8
if (FALSE) linearRelation(mydata, x = "pm10", y = "pm25", rsq.thresh = 0.8)
```