Multiple linear regression in therapeutic study I performed a therapeutic study with mice. Mice were divided into 5 group. The dependent variable of my study is tumor volume which is I measured every 2 days. The result is this.

After that, I performed multiple linear regression using variable group (e.g. control, Ab only, etc.) and day.
Call:
lm(formula = Volume ~ Group + Day, data = rpmi)

Residuals:
    Min      1Q  Median      3Q     Max 
 -1233.5  -303.7   -46.0   221.3  4828.3 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1224.90      89.88  13.628  < 2e-16 ***
GroupAb only -1052.18      98.26 -10.709  < 2e-16 ***
GroupPIT100  -1230.10      98.84 -12.445  < 2e-16 ***
GroupPIT500  -1304.88     100.84 -12.940  < 2e-16 ***
GroupYttrium -1417.04      95.92 -14.773  < 2e-16 ***
Day             17.55       3.04   5.772 1.47e-08 ***

Is it a legitimate way to compare the effect of the treatment? I am trying to find the reference but other paper usually performed ANOVA on last day of treatment only. Thank you 
 A: Yusri,
I don't think that using multiple regression here makes sense and certainly not in this manner. The dummies for the treatments tell you the average difference between the tumor size in the control and the treatment over the entire period. I don't see why that's relevant. Wouldn't you be more interested in the effect of the treatment on the tumor size at the end of the treatment?
In addition the model seems to be misspecified. The residuals will be increasing with time if I am not mistaken. I suspect that the errors are heteroscedastic due to the wrong functional form specification. 
I think that comparing the difference between treatment and control at the end plus this figure is all the evidence you need to convince the reader.
A: If you measured each mouse at two day intervals then your analysis is not appropriate as it does not take that fact into account. You need to investigate mixed effect models. You would have two fixed effects, group and day, and a random effect for mouse to remove the effect of individual variability between mice. You might also need a random slope for day to take account of individual variability in growth rate between mice. Software advice is off-topic here but since you use R you could investigate the nlme package which comes with your installation although there are other options.
A: You could analyze it as a repeated measures ANOVA and test specifically for the group x days (linear) interaction. It's OK if the relationship is not linear since the linear component will usually capture most of the variance if the relationship is monotonic. One method is to compute the linear component for each subject and then do an ANOVA and use Dunnett's test to compare each mean with the control (regardless of whether the ANOVA is significant). 
