Chapter1.R

### Project: inch through a calculus text with R as my graphing calculator. Noted: R is not a graphing calculator.
 
## Ch 1.2
 
### Problem 21
 
q21 <- read.table(text = "
income           ulcer_rate
4000             14.1
6000             13.0
8000             13.4
12000            12.5
16000            12.0
20000            12.4
30000            10.5
45000            9.4
60000            8.2
",header = TRUE, sep = "")
 
plot.window(c(0,15), c(0,80000))
plot(q21, ylim = c(0,15), xlim = c(0,80000))
 
#### Brute Force linear model
rise <- q21[nrow(q21),2] - q21[1,2]
run <-  q21[nrow(q21),1] - q21[1,1]
slope <- rise/run
y_intercept <-  -1 * (slope * q21[nrow(q21),1] - q21[nrow(q21),2])
b <- c(y_intercept, -1 * (slope * q21[1,1] - q21[1,2])) ## just checking
part_b <- function(x) {return (slope * x + y_intercept)}
 
abline(a = y_intercept, b = slope, col = "lightblue") ## linear model
 
abline(lsfit(q21$income, q21$ulcer_rate), col = "pink") ## least squares
abline(lm(q21$ulcer_rate ~ q21$income), col = "grey40") ## also draws least squares
#### the tilde you can think of as "depends on" -- population depends on year.
 
part_b(80000) ## ulcer rate at $80K?
 
### Problem 22
 
q22 <- read.table(text = "
temperature        chirps_per_min
50                 20
55                 46
60                 79
65                 91
70                 113
75                 140
80                 173
85                 198
90                 211
",header = TRUE, sep = "")
 
plot(q22, ylim=c(0,300), xlim = c(32,110))
abline(lsfit(q22$temperature, q22$chirps_per_min))
 
abline(lm(q22$chirps_per_min ~ q22$temperature))
 
#### Sanity check: Calculate my own slope using two points closest to the line
slope <- ((q22[2,2] - q22[6,2]) / (q22[2,1] - q22[6,1]))
 
new.temp <- data.frame(temperature = 100)
model <- lm(chirps_per_min ~ temperature, data = q22)
predict(model, newdata = new.temp)
 
points(100,264.7) ## Draw the result on the line, just to see. 
 
### Problem 24
 
q23 <- read.table(text = "
      Year  Height_in_feet
      1900	10.83
      1904	11.48
      1908	12.17
      1912	12.96
      1920	13.42
      1924	12.96
      1928	13.77
      1932	14.15
      1936	14.27
      1948	14.1
      1952	14.92
      1956	14.96
      1960	15.42
      1964	16.73
      1968	17.71
      1972	18.04
      1976	18.04
      1980	18.96
      1984	18.85
      1988	19.77
      1992	19.02
      1996	19.42
                  ",header = TRUE, sep = "")
 
plot(q23)
 
model <- lm(Height_in_feet ~ Year, data = q23)
abline(model)
new.data <- data.frame(Year = c(2000, 2010, 2100))
 
predict(model, newdata = new.data)
 
### Problem 24
 
 
## /* 'Reduction in emissions (%)'  'Cost per car (in $)' */
    q24 <- read.table(text = "reductions  cost.per.car
        50	45
        55	55
        60	62
        65	70
        70	80
        75	90
        80	100
        85	200
        90	375
        95	600
        ",header = TRUE, sep = "")
 
plot(q24$cost.per.car, q24$reductions, ylim = c(0,100), xlim = c(0,700))
 
#### Looks exponential, but how do I model that?
 
### Problem 25
 
q25 <- read.table(text = "year  pop.in.millions
                  1900	1650
                  1910	1750
                  1920	1860
                  1930	2070
                  1940	2300
                  1950	2560
                  1960	3040
                  1970	3710
                  1980	4450
                  1990	5280
                  2000	6070",header = TRUE, sep = "")
 
plot(q25, ylim=c(0, 8000))
 
 
#### Looks cubic, but how do you model that? 
model <- lm(pop.in.millions ~ poly(year, degree=3), data=q25)
abline(model)
 
### Problem 26
 
q26 <- read.table(text = "
Planet  d  T
Mercury	0.387	0.241
Venus	0.723	0.615
Earth	1	1
Mars	1.523	1.881
Jupiter	5.203	11.861
Saturn	9.541	29.457
Uranus	19.19	84.008
Neptune	30.086	164.784
",header = TRUE, sep = "")
 
plot(q26$d, q26$T)