library(readxl)
library(ggplot2)
library(RColorBrewer)
library(magrittr)
library(tidyverse)

Loading and Transforming the data

dataset <- read_excel("Coins.xlsx") 
df <- dataset[c(1:4)]
df %>% head( .,4)
## # A tibble: 4 x 4
##   Coin             Condition Mintage Value
##   <chr>            <chr>       <dbl> <dbl>
## 1 1878, 8 feathers VF-20      749500    85
## 2 1878, 8 feathers EF-40      749500   100
## 3 1878, 8 feathers AU-50      749500   120
## 4 1878, 8 feathers MS-60      749500   200
 df3 <- df %>% 
  mutate(log_val = log2(Value),
         log_Mintage = log2(Mintage)) 
 
df3 <- df3%>% filter( Condition != "PF-63")
attach(df3)
Condition1 = as.factor(df3$Condition)
val <- levels(Condition1)
Condition2 <- relevel(Condition1, ref= "VF-20")

Fit of the model

attach(df3)
## The following objects are masked from df3 (pos = 3):
## 
##     Coin, Condition, log_Mintage, log_val, Mintage, Value
model3 <- lm(log_val ~ Condition2 + log_Mintage+ Condition2:log_Mintage, data = df3)
summary(model3)
## 
## Call:
## lm(formula = log_val ~ Condition2 + log_Mintage + Condition2:log_Mintage, 
##     data = df3)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6194 -1.0392 -0.2207  0.5179  8.9794 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 20.27817    2.24486   9.033  < 2e-16 ***
## Condition2AU-50              3.97420    3.17471   1.252 0.211096    
## Condition2EF-40              1.83729    3.17471   0.579 0.562980    
## Condition2MS-60              9.21522    3.17471   2.903 0.003829 ** 
## Condition2MS-63             10.01337    3.17471   3.154 0.001687 ** 
## Condition2MS-64             10.42315    3.17471   3.283 0.001083 ** 
## Condition2MS-65             11.23284    3.17471   3.538 0.000432 ***
## log_Mintage                 -0.65650    0.10273  -6.391 3.21e-10 ***
## Condition2AU-50:log_Mintage -0.14348    0.14528  -0.988 0.323723    
## Condition2EF-40:log_Mintage -0.06909    0.14528  -0.476 0.634549    
## Condition2MS-60:log_Mintage -0.33433    0.14528  -2.301 0.021697 *  
## Condition2MS-63:log_Mintage -0.34123    0.14528  -2.349 0.019139 *  
## Condition2MS-64:log_Mintage -0.32933    0.14528  -2.267 0.023735 *  
## Condition2MS-65:log_Mintage -0.29861    0.14528  -2.055 0.040244 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.903 on 630 degrees of freedom
## Multiple R-squared:  0.6041, Adjusted R-squared:  0.5959 
## F-statistic: 73.95 on 13 and 630 DF,  p-value: < 2.2e-16

It can be seen that p-value of the F-statistic is 5.627e-09, which is highly significant. This means that, at least, one of the predictor variables is significantly related to the outcome variable.

Plots

#Histograms

par(mfrow = c(1,2))
hist(log_val,col="yellow")

hist(log_Mintage,col="cyan")

#Scatterplot

scat <- ggplot(df3, aes(log_Mintage, log_val, colour = factor(Condition))) +
  geom_point()

scat + facet_grid(. ~ Condition, scales = "free")

#boxplot

ggplot(df3, aes(x=as.factor(Condition), y=log_val)) + 
  geom_boxplot( fill = "slateblue " , alpha=0.2) + 
  xlab("Condition")