polynomial fitting and plotting regression line in R

Question

I am trying to find orthogonal polynomials of degree 3 for my data. The purpose of this is that i would like to visualise different polynomials fittings on my data: degree 3 and degree 7. I am using the same code as our profesor in class, however I cannot obtain nice results.

orthpoly <- poly(Air_reduced$Temp, order=3)
Air_reduced$xo1 <- orthpoly[,1]
Air_reduced$xo2 <- orthpoly[,2]
Air_reduced$xo3 <- orthpoly[,3]

polymodel1 <- lm(Ozone ~ xo1 + xo2 + xo3, data=Air_reduced)
Air_reduced$fitted1 <- fitted(polymodel1)

?plot
plot(Air_reduced$Temp,Air_reduced$Ozone,xlab="x",ylab="f(x)",
     cex.lab=1.5,cex.axis=1.3,col="red",cex=1.3,
     main="Polynomial of degree 3", xlim = c(50,97), ylim = c(0,100))
lines(Air_reduced$Temp, Air_reduced$fitted1,col="blue",lwd=3)

however this produces an ugly graph. There seem to be numerous regression lines.

What am i doing wrong?

Data:

structure(list(Ozone = c(41L, 36L, 12L, 18L, 23L, 19L, 8L, 16L, 
11L, 14L, 18L, 14L, 34L, 6L, 30L, 11L, 1L, 11L, 4L, 32L, 23L, 
45L, 37L, 29L, 71L, 39L, 23L, 21L, 37L, 20L, 12L, 13L, 49L, 32L, 
64L, 40L, 77L, 97L, 97L, 85L, 10L, 27L, 7L, 48L, 35L, 61L, 79L, 
63L, 16L, 80L, 108L, 20L, 52L, 82L, 50L, 64L, 59L, 39L, 9L, 16L, 
122L, 89L, 110L, 44L, 28L, 65L, 22L, 59L, 23L, 31L, 44L, 21L, 
9L, 45L, 73L, 76L, 118L, 84L, 85L, 96L, 78L, 73L, 91L, 47L, 32L, 
20L, 23L, 21L, 24L, 44L, 21L, 28L, 9L, 13L, 46L, 18L, 13L, 24L, 
16L, 13L, 23L, 36L, 7L, 14L, 30L, 14L, 18L, 20L), Solar.R = c(190L, 
118L, 149L, 313L, 299L, 99L, 19L, 256L, 290L, 274L, 65L, 334L, 
307L, 78L, 322L, 44L, 8L, 320L, 25L, 92L, 13L, 252L, 279L, 127L, 
291L, 323L, 148L, 191L, 284L, 37L, 120L, 137L, 248L, 236L, 175L, 
314L, 276L, 267L, 272L, 175L, 264L, 175L, 48L, 260L, 274L, 285L, 
187L, 220L, 7L, 294L, 223L, 81L, 82L, 213L, 275L, 253L, 254L, 
83L, 24L, 77L, 255L, 229L, 207L, 192L, 273L, 157L, 71L, 51L, 
115L, 244L, 190L, 259L, 36L, 212L, 215L, 203L, 225L, 237L, 188L, 
167L, 197L, 183L, 189L, 95L, 92L, 252L, 220L, 230L, 259L, 236L, 
259L, 238L, 24L, 112L, 237L, 224L, 27L, 238L, 201L, 238L, 14L, 
139L, 49L, 20L, 193L, 191L, 131L, 223L), Wind = c(7.4, 8, 12.6, 
11.5, 8.6, 13.8, 20.1, 9.7, 9.2, 10.9, 13.2, 11.5, 12, 18.4, 
11.5, 9.7, 9.7, 16.6, 9.7, 12, 12, 14.9, 7.4, 9.7, 13.8, 11.5, 
8, 14.9, 20.7, 9.2, 11.5, 10.3, 9.2, 9.2, 4.6, 10.9, 5.1, 6.3, 
5.7, 7.4, 14.3, 14.9, 14.3, 6.9, 10.3, 6.3, 5.1, 11.5, 6.9, 8.6, 
8, 8.6, 12, 7.4, 7.4, 7.4, 9.2, 6.9, 13.8, 7.4, 4, 10.3, 8, 11.5, 
11.5, 9.7, 10.3, 6.3, 7.4, 10.9, 10.3, 15.5, 14.3, 9.7, 8, 9.7, 
2.3, 6.3, 6.3, 6.9, 5.1, 2.8, 4.6, 7.4, 15.5, 10.9, 10.3, 10.9, 
9.7, 14.9, 15.5, 6.3, 10.9, 11.5, 6.9, 13.8, 10.3, 10.3, 8, 12.6, 
9.2, 10.3, 10.3, 16.6, 6.9, 14.3, 8, 11.5), Temp = c(67L, 72L, 
74L, 62L, 65L, 59L, 61L, 69L, 66L, 68L, 58L, 64L, 66L, 57L, 68L, 
62L, 59L, 73L, 61L, 61L, 67L, 81L, 76L, 82L, 90L, 87L, 82L, 77L, 
72L, 65L, 73L, 76L, 85L, 81L, 83L, 83L, 88L, 92L, 92L, 89L, 73L, 
81L, 80L, 81L, 82L, 84L, 87L, 85L, 74L, 86L, 85L, 82L, 86L, 88L, 
86L, 83L, 81L, 81L, 81L, 82L, 89L, 90L, 90L, 86L, 82L, 80L, 77L, 
79L, 76L, 78L, 78L, 77L, 72L, 79L, 86L, 97L, 94L, 96L, 94L, 91L, 
92L, 93L, 93L, 87L, 84L, 80L, 78L, 75L, 73L, 81L, 76L, 77L, 71L, 
71L, 78L, 67L, 76L, 68L, 82L, 64L, 71L, 81L, 69L, 63L, 70L, 75L, 
76L, 68L), Month = c(5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 
6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 
8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
9L, 9L), Day = c(1L, 2L, 3L, 4L, 7L, 8L, 9L, 12L, 13L, 14L, 15L, 
16L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 28L, 29L, 31L, 7L, 
9L, 10L, 13L, 16L, 17L, 18L, 19L, 20L, 2L, 3L, 5L, 6L, 7L, 8L, 
9L, 10L, 12L, 13L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 24L, 25L, 
26L, 27L, 28L, 29L, 30L, 31L, 1L, 2L, 3L, 7L, 8L, 9L, 12L, 13L, 
14L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 24L, 26L, 28L, 29L, 30L, 
31L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 
14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 
28L, 29L, 30L), ID = c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 
11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L, 22L, 24L, 
25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 35L, 36L, 37L, 38L, 
39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 
52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 
65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 78L, 
79L, 80L, 81L, 82L, 83L, 84L, 85L, 86L, 87L, 88L, 89L, 90L, 91L, 
92L, 93L, 94L, 95L, 96L, 97L, 98L, 99L, 100L, 101L, 102L, 103L, 
104L, 105L, 106L, 107L, 108L, 109L, 110L, 111L)), .Names = c("Ozone", 
"Solar.R", "Wind", "Temp", "Month", "Day", "ID"), row.names = c(NA, 
-108L), class = c("tbl_df", "tbl", "data.frame"))

Answer 1

Order your data by your x-axis before plotting, and your plot will be pretty:

Air_reduced = Air_reduced[order(Air_reduced$Temp), ]

As a side note, I'd encourage you to try out ggplot2 for plotting. It can fit simple models and plot all at once, and it's smart about defaults (default labels, default ordering the points when plotting a line...). In this case, if you just want a plot with both polynomials, it takes just a few lines of code:

library(ggplot2)
ggplot(Air_reduced, aes(x = Temp, y = Ozone)) +
  geom_point(color = "red") +
  stat_smooth(method = "lm",
              formula = y ~ poly(x, 3),
              aes(color = "3rd")) +
  stat_smooth(method = "lm",
              formula = y ~ poly(x, 7),
              aes(color = "7th")) +
  scale_color_manual(
    name = "Polynomial Degree",
    breaks = c("3rd", "7th"),
    values = c("blue", "green4")
  )