# Model Building: Missing Data or Large Gap between data points

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.

• Draw two regression lines, one for each set of data. – Peter Flom - Reinstate Monica May 12 '13 at 17:41
• Did you mean one with the log and one without? – add-semi-colons May 12 '13 at 17:51
• I didn't see your log graph when I posted my comment. I meant divide the data set in two where the gap is; but if taking the log of both variables makes sense, that works too. – Peter Flom - Reinstate Monica May 12 '13 at 18:00
• Any technique to divide data into two sets? – add-semi-colons May 12 '13 at 18:07
• Just split them at the big gap. – Peter Flom - Reinstate Monica May 12 '13 at 19:00