# If the datapoint furthest from the y‐axis was excluded, what would happen to the associations seen?

looking at the Figure below, what would happen to the association if the datapoint furtherst from the y-axis was excluded?

Current linear association indicates: Diabetes prev = -0.0171183 x BT consumption + 6173.61

Refernce: Beresniak A, Duru G, Berger G, et alRelationships between black tea consumption and key health indicators in the world: an ecological studyBMJ Open 2012;2:e000648. doi: 10.1136/bmjopen-2011-000648

• With this amount of data, it should be fairy easy to extract the data points with software such as WebPlotDigitizer. You can then remove one data point, redo the analysis, and find the answer to your question. – Sal Mangiafico Oct 19 '19 at 13:30

I tried to replicate the data using WebPlotDigitizer. These values are approximate, and I'm not sure I captured all data points. I ended up with an n of 40.

You might be surprised that the linear model doesn't change much with that one point removed. Without that one point, the best-fit line is similar, and actually the p value decreases a tad and the r-squared increases a bit.

There may be some other problems with fitting a simple linear model to these data. The residuals are not particularly normal, and the data are not particularly homeoscedastic.

R code below. You can run it at: https://rdrr.io/snippets/ or in R.

Data = read.table(header=TRUE, text="
X Y
1.1965811965811959  12.870229007633586
0.04273504273504258 9.34351145038168
0                   8.427480916030532
0.5128205128205128  8.335877862595419
21.581196581196576  2.65648854961832
18.119658119658116  5.0381679389312986
16.58119658119658   3.206106870229009
9.615384615384613   3.9389312977099245
10.641025641025639  3.9389312977099245
7.350427350427348   6.137404580152671
3.7606837606837606  6.870229007633588
1.4102564102564097  6.961832061068703
0.04273504273504258 6.641221374045802
0.17094017094017122 6.595419847328243
0                   6.137404580152671
0.6837606837606831  6.137404580152671
1.6239316239316235  6.320610687022901
3.0769230769230766  6.091603053435115
4.786324786324786   5.404580152671755
0.6837606837606831  5.679389312977099
1.0256410256410255  5.9541984732824424
1.282051282051282   5.7251908396946565
1.4529914529914523  5.358778625954198
1.4529914529914523  5.587786259541986
0.04273504273504258 5.221374045801527
0.4273504273504267  5.221374045801527
0.6837606837606831  5.404580152671755
0.2136752136752138  4.48854961832061
0.6837606837606831  4.9465648854961835
1.0683760683760681  5.0381679389312986
1.1965811965811959  4.992366412213741
1.7094017094017095  4.809160305343513
1.0256410256410255  5.404580152671755
2.051282051282051   1.8778625954198471
3.1623931623931627  4.580152671755725
4.700854700854701   1.8778625954198471
4.444444444444444   4.305343511450381
5.470085470085469   4.2595419847328255
7.777777777777776   3.1603053435114514
3.0769230769230766  5.587786259541986
")

plot(Y ~ X, data=Data, pch=3)
abline(6.13064, -0.17048, col="black")

model = lm(Y ~ X, data=Data)

summary(model)

### Original model
### slope     = -0.17
### p         = 0.004
### r-squared = 0.198

Data2 = Data[2:40,]

plot(Y ~ X, data=Data2, pch=20)
abline(5.89043, -0.15360, col="blue")

model2 = lm(Y ~ X, data=Data2)

summary(model2)

### Second model
### slope     = -0.15
### p         = 0.001
### r-squared = 0.252