permeability correction from core scale to log scale using simple linear regression

# imort data
data = read.csv('C:/Users/intel/Desktop/karpur.csv')

# difine some required data and convert phi.core to fraction
kcore= data$k.core
phi.N= data$phi.N
phi.core= data$phi.core/100

# plot the relationship between porosity from log and porosity from core
plot(phi.N,phi.core,main='scatterplot')

# plot best strighat line between porosity from log and porosity from core
mod1=lm(phi.core ~ phi.N )
summary(mod1)

## 
## Call:
## lm(formula = phi.core ~ phi.N)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.135237 -0.030779  0.009432  0.033563  0.104025 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.30962    0.00485  63.846   <2e-16 ***
## phi.N       -0.18207    0.02080  -8.753   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04368 on 817 degrees of freedom
## Multiple R-squared:  0.08573,    Adjusted R-squared:  0.08462 
## F-statistic: 76.61 on 1 and 817 DF,  p-value: < 2.2e-16

abline(mod1)

# corected values of phi core
phi.core_to_log=predict(mod1)

# check that kcore is normal or not
hist(kcore,breaks = 10)

# upply log to optain normal distrbution
hist((log(kcore)),breaks = 10)

# plot the relationship between phi.core_to_log and log(kcore) and plot best strait line between them 
plot(phi.core_to_log,log(kcore))
mod2=lm(log(kcore) ~ phi.core_to_log)
abline(mod2)

k_log=predict(mod2)

summary(k_log)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   6.057   6.885   6.993   7.128   7.232   8.298