# Solved – Comparing two linear regression models

model comparisonregression

I would like to compare two linear regression models which represent degradation rates of a mRNA over time under two different conditions. The data for each model collected independently.

Here is the dataset.

Time (hours)    log(Treatment A)     log(treatment B)
0   2.02    1.97
0   2.04    2.06
0   1.93    1.96
2   2.02    1.91
2   2.00    1.95
2   2.07    1.82
4   1.96    1.97
4   2.02    1.99
4   2.02    1.99
6   1.94    1.90
6   1.94    1.97
6   1.86    1.88
8   1.93    1.97
8   2.12    1.99
8   2.06    1.93
12  1.71    1.70
12  1.96    1.73
12  1.71    1.76
24  1.70    1.46
24  1.83    1.41
24  1.62    1.42


These are my models:

Exp1.A.lm<-lm(Exp1$$Time~Exp1$$(Treatment A))
Exp1.B.lm<-lm(Exp1$$Time~Exp1$$(Treatment B))

Call:
lm(formula = Exp1$$Time ~ Exp1$$(Treatment A))

Residuals:
Min      1Q  Median      3Q     Max
-6.8950 -1.2322  0.2862  1.2494  5.2494

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)           74.68       6.27   11.91 2.94e-10 ***
Exp1$(Treatment A) -36.14 3.38 -10.69 1.77e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.97 on 19 degrees of freedom Multiple R-squared: 0.8575, Adjusted R-squared: 0.85 F-statistic: 114.3 on 1 and 19 DF, p-value: 1.772e-09 Call: lm(formula = Exp1$$Time ~ Exp1$$(Treatment B)) Residuals: Min 1Q Median 3Q Max -7.861 -3.278 -1.444 3.222 11.972 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 88.281 16.114 5.478 2.76e-05 *** Exp1$(Treatment B)  -41.668      8.343  -4.994 8.05e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.173 on 19 degrees of freedom
Multiple R-squared: 0.5676, Adjusted R-squared: 0.5449
F-statistic: 24.94 on 1 and 19 DF,  p-value: 8.052e-05


To compare these two models, I used this following code.

anova(Exp1.A.lm,Exp1.B.lm)

Analysis of Variance Table

Model 1: Exp1$$Time ~ Exp1$$Exp1$$(Treatment A) Model 2: Exp1$$Time ~ Exp1$$Exp1$$(Treatment B)
Res.Df    RSS Df Sum of Sq F Pr(>F)
1     19 167.60
2     19 508.48  0   -340.88

My question is why the ANOVA analysis doesn't show an F statistics and a p.val. My apologies if this is a naive question.

Based on different slopes, the rate of degradation is different in these two models, but I would like to know how statistically significant this difference is. I hope that this makes sense.