I am currently trying to build a model using a data set that has large gap between data points. When I look for the correlation I clearly see a negative regression line. But I am worried about the gap that exist between the poins.
I build a simple linear model though this has high R squared I don't think simple linear regression is the best model to that fits the data. This looks like it has a negative exponential behavior. I thought to post here to get some expert thoughts on what I should do when you deal with the data that has a large gap between points and does this data has a linear relationship or strong non linear relationship?
Data Set:
density co2
1 20.4 38.8
2 27.4 31.5
3 106.2 10.6
4 80.4 16.1
5 141.3 7.7
6 130.9 8.3
7 121.7 8.5
8 106.5 11.1
9 130.5 8.6
10 101.1 11.1
11 123.9 9.8
12 144.2 7.8
13 29.5 31.8
14 30.8 31.6
15 26.5 34.0
16 35.7 28.9
17 30.0 28.8
18 106.2 10.5
19 97.0 12.3
20 90.1 13.2
21 106.7 11.4
22 99.3 11.2
23 107.2 10.3
24 109.1 11.4
Plot:
Summary of Linear Model:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 38.12948 1.21768 31.31 < 2e-16 ***
density -0.24247 0.01261 -19.22 3.04e-15 ***
In addition if I transfer both density and co2 as log transform variables, then I see following behavior. Since data is missing at the middle its really hard to stick to a log transformed model or the base model.