**trend analysis**with the Cox-Stuart test and on simple linear regression. The goal that we propose is to assess the trend in the number of visits received from a site over a long time. I use

*Google Analytics*, because this tool allows us to save the various reports in

*Excel CSV format*. Let's see, step by step, how to save the reportage, and then

**how to import data from Excel to R**, and finally how to estimate if the number of daily visitors follows an increasing or decreasing trend.

Let's start by creating an ad hoc report in Google Analytics. Once you have logged in, select the date range that we want to analyze. Then click on

*Visits*.

At this point we can save the report, clicking on

*Export*and then clicking on

**CSV for Excel**.

Save the CSV file, and open it with Excel. Here's how it seems:

Now import the data into R. Import data from Excel to R is very simple. Simply select the column (or columns) of our interest (in our case the column

`Visits`

) and copy in the clipboard with CTRL + C (remember to select the cell `Visits`

, because it will be useful):Then open R and type the following command:

myvisit <- read.delim("clipboard")

myvisit

Visits

1 33

2 41

3 34

4 45

5 46

6 37

7 31

8 37

9 34

10 34

11 48

12 39

13 33

...

It is a one column dataframe; the name of the column is Visits (so it is importat to select the header from Excel).

Now we can proceed with the analysis of trends in the two proposed ways: through a

**Cox-Stuart test**e through the

**analysis of the simple linear regression**.

The function to perform the Cox-Stuart test is available here. First we must convert the dataframe in a format that can be read by the function cox.stuart.test, like this:

visits <- c(myvisit$Visits)

I have created in this way, a vector (visits) that contains all data that were ordered in the column Visits of the dataframe myvisit. Now we provide a test of Cox-Stuart:

cox.stuart.test(visits)

Cox-Stuart test for trend analysis

data:

Increasing trend, p-value = 0.0012

The output is very clear: We have detected an increasing trend of visits, highly significant (since

*p-value < 0.5*).

If we are not satisfied or sure of this result, we can take into account the slope of the regression line. Firstly may want to show the results. The vector contains the hits daily visits to the site. Now we create a sorted array of the days in question, the same length of the carrier hits:

days <- c(1 : length(visits))

Create a plot:

plot(days, visits, type="b")

Choosing

`type="b"`

I see dots and lines, as shown in figure:From this plot is not easy to observe a possible trend of the progress of visits. We can still do a regression analysis. Evaluating the sign of the slope of the line, we can estimate whether the trend is increasing or decreasing:

fit <- lm(visits ~ days)

summary(fit)

Call:

lm(formula = visits ~ days)

Residuals:

Min 1Q Median 3Q Max

-22.714 -6.197 -1.313 5.648 31.153

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 31.79694 2.27151 13.998 < 2e-16 ***

days 0.19815 0.04242 4.671 1.04e-05 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.81 on 90 degrees of freedom

Multiple R-squared: 0.1951, Adjusted R-squared: 0.1862

F-statistic: 21.82 on 1 and 90 DF, p-value: 1.043e-05

The slope coefficient has a value of:

`b = 0.06251`

. It therefore has a positive sign, then one may think of an increasing trend. The value of the statistical t-test on the slope, and its relative p-value, indicate either that it is significant. We can therefore say that there is an increasing trend.Finally, we can see the regression line directly on the plot previously obtained in this way:

plot(days, visits, type="b")

abline(fit, col="red", lwd=3)

The command abline allows us to add a line defined by the equation given, directly on the chart shown; the parameter "col" specifies the color and the "lwd" parameter specifies the thickness of the line. Observe now the graph:

It's obvious that there is an increasing trend, as said by the Cox-Stuart test.

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