0
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This is probably a very basic question on statistics, but somehow I can’t understand it in a way that I’m sure that my interpretation of the outcome will be correct. Here goes.

I have data on the visits to two webpages that are part of the same domain. I have daily data on visits for a whole year. I’ve made visualisations of the rolling mean for both pages in one graph. However, people seem to interpret these different. One person sees a strong connection in visits to one and the other, another person does not. I’m now looking for a statically solid way to settle this.

Basically I want to know if an increase/decrease in one is linked to increase/decrease in the other over time. I’ve looked into correlation/covariance but I’m thrown off by that they need to be linear? Since the visits increase and decrease depending on the day, there is no such thing.

I’m using R Studio for my graphs and data cleaning/processing. I have one column with dates (one date for each page), one that identifies the page (page1, page2), one with the number of visits and one with the rolling 7-day mean.

Thanks in advance!

Data:

structure(list(Date = structure(c(18628, 18628, 18627, 18627, 
18626, 18626, 18625, 18625, 18624, 18624, 18623, 18623, 18622, 
18622, 18621, 18621, 18620, 18620, 18619, 18619, 18618, 18618, 
18617, 18617, 18616, 18616, 18615, 18615, 18614, 18614, 18613, 
18613, 18612, 18612, 18611, 18611, 18610, 18610, 18609, 18609, 
18608, 18608, 18607, 18607, 18606, 18606, 18605, 18605, 18604, 
18604, 18603, 18603, 18602, 18602, 18601, 18601, 18600, 18600, 
18599, 18599, 18598, 18598, 18597, 18597, 18596, 18596, 18595, 
18595, 18594, 18594, 18593, 18593, 18592, 18592, 18591, 18591, 
18590, 18590, 18589, 18589, 18588, 18588, 18587, 18587, 18586, 
18586, 18585, 18585, 18584, 18584, 18583, 18583, 18582, 18582, 
18581, 18581, 18580, 18580, 18579, 18579, 18578, 18578, 18577, 
18577, 18576, 18576, 18575, 18575, 18574, 18574, 18573, 18573, 
18572, 18572, 18571, 18571, 18570, 18570, 18569, 18569, 18568, 
18568, 18567, 18567, 18566, 18566, 18565, 18565, 18564, 18564, 
18563, 18563, 18562, 18562, 18561, 18561, 18560, 18560, 18559, 
18559, 18558, 18558, 18557, 18557, 18556, 18556, 18555, 18555, 
18554, 18554, 18553, 18553, 18552, 18552, 18551, 18551, 18550, 
18550, 18549, 18549, 18548, 18548, 18547, 18547, 18546, 18546, 
18545, 18545, 18544, 18544, 18543, 18543, 18542, 18542, 18541, 
18541, 18540, 18540, 18539, 18539, 18538, 18538, 18537, 18537, 
18536, 18536, 18535, 18535, 18534, 18534, 18533, 18533, 18532, 
18532, 18531, 18531, 18530, 18530, 18529, 18529, 18528, 18528, 
18527, 18527, 18526, 18526, 18525, 18525, 18524, 18524, 18523, 
18523, 18522, 18522, 18521, 18521, 18520, 18520, 18519, 18519, 
18518, 18518, 18517, 18517, 18516, 18516, 18515, 18515, 18514, 
18514, 18513, 18513, 18512, 18512, 18511, 18511, 18510, 18510, 
18509, 18509, 18508, 18508, 18507, 18507, 18506, 18506, 18505, 
18505, 18504, 18504, 18503, 18503, 18502, 18502, 18501, 18501, 
18500, 18500, 18499, 18499, 18498, 18498, 18497, 18497, 18496, 
18496, 18495, 18495, 18494, 18494, 18493, 18493, 18492, 18492, 
18491, 18491, 18490, 18490, 18489, 18489, 18488, 18488, 18487, 
18487, 18486, 18486, 18485, 18485, 18484, 18484, 18483, 18483, 
18482, 18482, 18481, 18481, 18480, 18480, 18479, 18479, 18478, 
18478, 18477, 18477, 18476, 18476, 18475, 18475, 18474, 18474, 
18473, 18473, 18472, 18472, 18471, 18471, 18470, 18470, 18469, 
18469, 18468, 18468, 18467, 18467, 18466, 18466, 18465, 18465, 
18464, 18464, 18463, 18463, 18462, 18462, 18461, 18461, 18460, 
18460, 18459, 18459, 18458, 18458, 18457, 18457, 18456, 18456, 
18455, 18455, 18454, 18454, 18453, 18453, 18452, 18452, 18451, 
18451, 18450, 18450, 18449, 18449, 18448, 18448, 18447, 18447, 
18446, 18446, 18445, 18445, 18444, 18444, 18443, 18443, 18442, 
18442, 18441, 18441, 18440, 18440, 18439, 18439, 18438, 18438, 
18437, 18437, 18436, 18436, 18435, 18435, 18434, 18434, 18433, 
18433, 18432, 18432, 18431, 18431, 18430, 18430, 18429, 18429, 
18428, 18428, 18427, 18427, 18426, 18426, 18425, 18425, 18424, 
18424, 18423, 18423, 18422, 18422, 18421, 18421, 18420, 18420, 
18419, 18419, 18418, 18418, 18417, 18417, 18416, 18416, 18415, 
18415, 18414, 18414, 18413, 18413, 18412, 18412, 18411, 18411, 
18410, 18410, 18409, 18409, 18408, 18408, 18407, 18407, 18406, 
18406, 18405, 18405, 18404, 18404, 18403, 18403, 18402, 18402, 
18401, 18401, 18400, 18400, 18399, 18399, 18398, 18398, 18397, 
18397, 18396, 18396, 18395, 18395, 18394, 18394, 18393, 18393, 
18392, 18392, 18391, 18391, 18390, 18390, 18389, 18389, 18388, 
18388, 18387, 18387, 18386, 18386, 18385, 18385, 18384, 18384, 
18383, 18383, 18382, 18382, 18381, 18381, 18380, 18380, 18379, 
18379, 18378, 18378, 18377, 18377, 18376, 18376, 18375, 18375, 
18374, 18374, 18373, 18373, 18372, 18372, 18371, 18371, 18370, 
18370, 18369, 18369, 18368, 18368, 18367, 18367, 18366, 18366, 
18365, 18365, 18364, 18364, 18363, 18363, 18362, 18362, 18361, 
18361, 18360, 18360, 18359, 18359, 18358, 18358, 18357, 18357, 
18356, 18356, 18355, 18355, 18354, 18354, 18353, 18353), class = "Date"), 
    BICOR2 = c("COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", 
    "COR", "REG", "COR", "REG", "COR", "REG", "COR", "REG", "COR", 
    "REG", "COR", "REG", "COR", "REG"), UPV = c(392, 33, 321, 
    43, 537, 71, 743, 86, 613, 93, 592, 75, 670, 66, 532, 40, 
    497, 46, 539, 69, 705, 92, 952, 105, 937, 132, 854, 78, 897, 
    136, 334, 37, 758, 126, 1555, 156, 1503, 135, 1902, 159, 
    1210, 74, 1095, 144, 698, 184, 930, 172, 835, 194, 355, 148, 
    584, 92, 402, 54, 449, 128, 630, 171, 887, 146, 856, 223, 
    876, 234, 617, 79, 597, 64, 602, 132, 732, 219, 884, 196, 
    874, 220, 703, 210, 612, 107, 603, 82, 646, 125, 679, 152, 
    769, 149, 873, 139, 792, 175, 560, 117, 535, 69, 531, 126, 
    572, 135, 740, 117, 811, 170, 823, 155, 651, 76, 499, 79, 
    600, 113, 589, 132, 821, 159, 1518, 215, 1364, 195, 863, 
    110, 766, 112, 956, 150, 1102, 167, 1266, 212, 763, 175, 
    824, 206, 738, 97, 814, 78, 1139, 241, 1198, 221, 1090, 187, 
    1240, 224, 1300, 195, 1034, 120, 1011, 109, 1320, 183, 1740, 
    246, 2004, 260, 1727, 234, 1418, 239, 1167, 171, 981, 92, 
    1285, 195, 1612, 226, 1716, 263, 1894, 251, 2868, 442, 1730, 
    204, 2129, 208, 1693, 242, 1118, 256, 1107, 301, 1745, 310, 
    1696, 323, 846, 152, 732, 115, 872, 212, 1233, 252, 1099, 
    279, 909, 293, 948, 284, 780, 144, 795, 112, 1250, 177, 2213, 
    307, 1809, 305, 619, 160, 562, 186, 605, 125, 554, 94, 600, 
    121, 688, 157, 822, 206, 843, 194, 787, 170, 706, 118, 560, 
    73, 612, 105, 606, 153, 597, 146, 691, 161, 745, 151, 738, 
    81, 753, 90, 918, 138, 897, 128, 804, 129, 961, 168, 1018, 
    166, 935, 87, 1040, 112, 898, 157, 1009, 163, 1061, 137, 
    1311, 190, 1170, 179, 1234, 138, 1219, 128, 1292, 154, 1152, 
    181, 1349, 166, 1264, 148, 1430, 171, 1364, 134, 1354, 128, 
    1784, 157, 2682, 300, 1326, 139, 1581, 167, 1710, 169, 1468, 
    169, 1199, 112, 1107, 142, 1355, 145, 1741, 196, 2147, 269, 
    2127, 234, 1940, 320, 1697, 273, 2019, 324, 2257, 362, 2227, 
    372, 2480, 451, 1925, 313, 2056, 273, 1678, 246, 2025, 286, 
    2148, 290, 1414, 235, 1628, 261, 1652, 76, 1780, 44, 1524, 
    40, 1664, 58, 1641, 60, 1666, 67, 1632, 85, 2020, 110, 2051, 
    52, 1613, 48, 1276, 102, 1442, 86, 1485, 105, 1640, 81, 1490, 
    125, 1604, 64, 1195, 49, 1270, 91, 1576, 111, 2213, 116, 
    2318, 131, 1311, 127, 856, 76, 778, 30, 724, 133, 712, 157, 
    737, 135, 844, 115, 1042, 164, 980, 89, 571, 55, 565, 102, 
    665, 90, 668, 114, 750, 115, 622, 168, 671, 63, 586, 68, 
    577, 122, 687, 134, 805, 170, 584, 115, 647, 100, 608, 71, 
    568, 66, 653, 103, 828, 164, 926, 176, 841, 135, 968, 143, 
    959, 88, 881, 79, 1044, 83, 1466, 60, 1217, 189, 945, 150, 
    1040, 121, 854, 106, 773, 62, 828, 142, 774, 138, 926, 137, 
    941, 156, 1193, 153, 982, 61, 688, 71, 934, 110, 1153, 137, 
    1179, 139, 760, 121, 910, 105, 632, 57, 573, 69, 603, 114, 
    792, 114, 1049, 120, 1058, 109, 808, 44, 647, 46, 567, 45, 
    627, 73, 820, 142, 1135, 118, 1184, 153, 822, 135, 674, 61, 
    581, 48, 694, 122, 830, 139, 1128, 118, 1461, 140, 1129, 
    87, 633, 62, 411, 65, 666, 101, 826, 152, 531, 110, 581, 
    144, 934, 161, 748, 70, 646, 54, 914, 117, 983, 172, 839, 
    151)), row.names = c(NA, -552L), class = c("tbl_df", "tbl", 
"data.frame"))
Improve this question
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3
  • 1
    $\begingroup$ This can be achieved with cross-correlation. Could you provide the data with dput(data) . Needed are date, number of visits page 1, number of visits site 2 $\endgroup$
    – Waldi
    Apr 23, 2021 at 17:07
  • $\begingroup$ @Waldi I added the data to my post, the pages 1 and 2 are in BICOR2 as REG and COR. Thanks! $\endgroup$
    – Justin
    Apr 24, 2021 at 13:12
  • $\begingroup$ @Justin, see my answer $\endgroup$
    – Waldi
    Apr 24, 2021 at 16:37

1 Answer 1

Reset to default
1
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First plotting the time series:

library(ggplot2)
ggplot(data)+geom_line(aes(x=Date,y=UPV,color=BICOR2))

enter image description here

Then running cross-correlation:

COR <- data[data$BICOR2 == "COR","UPV"]
REG <- data[data$BICOR2 == "REG","UPV"]

result <- ccf(COR, REG, type = 'correlation')

max(result$acf)
[1] 0.5838414

enter image description here

Best cross-correlation is achieved at 0 lag, with a significant correlation coefficient of 0.58.
As there is no lag, this suggests both pages visits depend on the same outside factors.

Improve this answer
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4
  • $\begingroup$ Since I expect the effect to be visible on the same day, the lag of 0 is what I’m most interested in, correct? In theory lag would be more interesting if I would be looking at data on rainfall and plant growth, where a change in one would cause a delayed reaction in the other. And what would be an insignificant correlations coefficient? $\endgroup$
    – Justin
    Apr 24, 2021 at 16:48
  • $\begingroup$ significance limit is the blue dashed line. Below this line : no correlation at all. For lag, this is indeed to show delayed reaction, but if you are only interested in the same day you could simply use cor(COR,REG). $\endgroup$
    – Waldi
    Apr 24, 2021 at 16:54
  • $\begingroup$ Great! Last questions: 1. The lack of negative correlation coefficients means there is no inverse relationship between the two? 2. What do the cc at different lags tell me? I don’t necessarily expect a relationship with a lag, so can these just occur at random? Since I presume the correlation occurs on the same date, I can discard them? $\endgroup$
    – Justin
    Apr 24, 2021 at 17:03
  • $\begingroup$ negative values would be anticorrelation : the first series goes up when the second one goes down. For the lagged values you see that correlation decreases, and this can be random. Try ccf(cos(2*pi*seq(1,360*3,by=15)/360),cos(2*pi*(30+seq(1,360*3,by=15))/360)) to better understand what is going on. $\endgroup$
    – Waldi
    Apr 24, 2021 at 17:33

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