1 Data Management

dtaHW1 <- read.table("C:/Users/ASUS/Desktop/data/freeRecall.asc.txt", h=T)
head(dtaHW1)
##   grp trial  ncr
## 1   C     1  7.9
## 2   C     2 10.9
## 3   C     3 11.9
## 4   C     4 13.0
## 5   C     5 14.2
## 6   C     6 14.2

2 NLS model

dta1_init <- c(a = 5, b = log(10/5))

summary(m0 <- nls(ncr~ a*exp(b*sqrt(trial)), data = dtaHW1,start = dta1_init))
## 
## Formula: ncr ~ a * exp(b * sqrt(trial))
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a  8.92939    0.50253  17.769 7.34e-13 ***
## b  0.17714    0.02269   7.806 3.47e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.864 on 18 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.602e-07

3 plot

library(ggplot2)
ggplot(dtaHW1, aes(trial, ncr, color = grp)) +
  stat_smooth(method = "nls", formula = y ~ a*exp(b*sqrt(x)), 
              method.args = list(start = dta1_init), 
              se = F,
              size = rel(.5)) +
  geom_point(pch = 1, size = rel(2)) +
  scale_x_continuous(limits = c(0, 10), breaks = seq(0, 10, by = 2)) +
  scale_y_continuous(limits = c(5, 20), breaks = seq(5, 20, by = 5)) +
  labs(x = "Trial on list B", 
       y = "Mean number of correct responses")

4 Residual

plot(m0)