Chapter 6 part2

library(mosaicCalc)

## Loading required package: mosaic

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## additional features.  The original behavior of these functions should not be affected by this.

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Families <- read.csv("http://www.mosaic-web.org/go/datasets/Income-Housing.csv")
gf_point(TwoVehicles ~ Income, data = Families)

kguess <- log(0.5) / 25000
kguess

## [1] -2.772589e-05

library(mosaic)

project( TwoVehicles ~ 1 + exp(Income*kguess), data = Families)

##          (Intercept) exp(Income * kguess) 
##             110.4263            -101.5666

library(mosaicCalc)
f <- makeFun( 110.43 - 101.57*exp(Income * k) ~ Income, k = kguess)
gf_point(TwoVehicles ~ Income, data = Families) %>%
  slice_plot(f(Income) ~ Income) 

f(Income = 10000)

## [1] 33.45433

f(Income = 50000)

## [1] 85.0375

Results <- Families %>% 
  dplyr::select(Income, TwoVehicles) %>%
  mutate(model_val = f(Income = Income),
         resids = TwoVehicles - model_val)
Results

##   Income TwoVehicles model_val     resids
## 1   3914        17.3  19.30528 -2.0052822
## 2  10817        34.3  35.17839 -0.8783904
## 3  21097        56.4  53.84097  2.5590313
## 4  34548        75.3  71.45680  3.8432013
## 5  51941        86.6  86.36790  0.2320981
## 6  72079        92.9  96.66273 -3.7627306

sum(Results$resids^2)

## [1] 40.32358

sum_square_resids <- Vectorize(function(k) {
  sum((Families$TwoVehicles - f(Income=Families$Income, k)) ^ 2)
})
slice_plot(
   sum_square_resids(k) ~ k, 
   domain(k = range(log(0.5)/40000,log(0.5)/20000)))