Visreg Plotting log-log as log-level - r

Question

I want to run a regression of money spent on links clicked using a data set where I notice link clicks level off after a certain amount of money spent. I want to use a log transformation to better fit this leveling-off data.
My data set looks like this:
link.clicks
[1] 34 60 54 49 63 100
MoneySpent
[1] 10.97 21.81 20.64 21.42 48.03 127.30
I want to predict the % change in link.clicks from a $1 increase in MoneySpent. My regression model is:
regClicksLogLevel <- lm(log(link.clicks) ~ (MoneySpent), data = TwtrData)
summary(regClicksLogLevel)
visreg(regClicksLogLevel)
However, The graph visreg generates looks like this:
[1]: https://i.stack.imgur.com/eZqVG.png
When I change my regression to:
regClicksLogLog <- lm(log(link.clicks) ~ log(MoneySpent), data = TwtrData)
summary(regClicksLogLog)
visreg(regClicksLogLog)
I actually get the fitted line I'm looking for:
[2]: https://i.stack.imgur.com/MexwC.png
I'm confused because I'm not trying to predict a % change in link.clicks from a % change in MoneySpent.
I'm trying to predict a % change in link.clicks from a $ unit change in MoneySpent.
Why can't I generate the 2nd graph using the my first regression, regClicksLogLevel?

Answer 1

I guess that's what you are looking for
library(tidyverse)
TwtrData = tibble(
link.clicks = c(34,60,54,49,63,100),
MoneySpent = c(10.97,21.81,20.64,21.42,48.03,127.30)
) %>% mutate(
perc.link.clicks = lag(link.clicks, default = 0)/link.clicks,
perc.MoneySpent = lag(MoneySpent, default = 0)/MoneySpent
)
regClicksLogLevel <- lm(perc.link.clicks ~ perc.MoneySpent, data = TwtrData)
summary(regClicksLogLevel)
output
Call:
lm(formula = perc.link.clicks ~ perc.MoneySpent, data = TwtrData)
Residuals:
1 2 3 4 5 6
-0.1422261 -0.0766939 -0.0839233 -0.0002346 0.1912170 0.1118608
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1422 0.1082 1.315 0.25890
perc.MoneySpent 0.9963 0.1631 6.109 0.00363 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1434 on 4 degrees of freedom
Multiple R-squared: 0.9032, Adjusted R-squared: 0.879
F-statistic: 37.32 on 1 and 4 DF, p-value: 0.003635
And here is the graph
TwtrData %>% ggplot(aes(perc.MoneySpent, perc.link.clicks))+
geom_line()+
geom_smooth(method='lm',formula= y~x)+
scale_y_continuous(labels = scales::percent)+
scale_x_continuous(labels = scales::percent)