knitr::opts_chunk$set(echo = TRUE)
# Create a data.frame object with examples of numeric, character, logical, and factor data types. Summarize the data.frame object in total as well as for each type within the text (e.g., in-text R component).
Height <- c(1.3, 1.6, 1.2, 1.8, 1.9)
Name <- c("John","Dora","Kevin","Mike", "Sarah")
IQ <- c("Smart", "Smart", "Dumb", "Smartest", "Dumbest")
Is.Doctor <- c(FALSE, FALSE, FALSE, TRUE, FALSE)
df1 <- as.data.frame(cbind(Height, Name, IQ, Is.Doctor))
summary(Height)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.20 1.30 1.60 1.56 1.80 1.90
summary(Name)
## Length Class Mode
## 5 character character
summary(IQ)
## Length Class Mode
## 5 character character
summary(Is.Doctor)
## Mode FALSE TRUE
## logical 4 1
summary(df1)
## Height Name IQ Is.Doctor
## 1.2:1 Dora :1 Dumb :1 FALSE:4
## 1.3:1 John :1 Dumbest :1 TRUE :1
## 1.6:1 Kevin:1 Smart :2
## 1.8:1 Mike :1 Smartest:1
## 1.9:1 Sarah:1
# Create 2 matrices of type numeric, each with 4 rows and 4 columns with 16 of your favorite numbers. In the text, describe the processes of matrix multiplication and kronecker products and demonstrate it with your example matrices.
x <- matrix(c(12,28,33,42,10,9,8,13,7,1,55,61,34,87,68,42),nrow=4)
z <- matrix(c(27,26,13,14,99,18,85,12,16,8,62,65,24,9,1,99),nrow=4)
# Matrix multiplication falls into two general categories. Scalar in which a single number is multiplied with every entry of a matrix and multiplication of an entire matrix by another entire matrix.
# Scalar Multiplication
x*2
## [,1] [,2] [,3] [,4]
## [1,] 24 20 14 68
## [2,] 56 18 2 174
## [3,] 66 16 110 136
## [4,] 84 26 122 84
# Matrix Multiplication can only be performed if the number of rows of the first matrix matches the number of columns of the second matrix. This is due to how each entry of the product matrix is calculated. Each number in the first row of the first matrix is multiplied by the corresponding number in the first coulmn of the second matrix and then summed.
x %*% z
## [,1] [,2] [,3] [,4]
## [1,] 1151 2371 2916 3751
## [2,] 2221 4063 6237 9367
## [3,] 2766 8902 8422 7651
## [4,] 2853 10081 7288 5344
#The Kronecker product is a different way to multiply two matrices. The second matrix is scalared by the first number in the first matrix and so on. If you multiply two 4x4 matrices then the resulting matrix will have 16 rows and 16 columns as shown below.
x %x% z
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 324 1188 192 288 270 990 160 240 189 693 112 168 918
## [2,] 312 216 96 108 260 180 80 90 182 126 56 63 884
## [3,] 156 1020 744 12 130 850 620 10 91 595 434 7 442
## [4,] 168 144 780 1188 140 120 650 990 98 84 455 693 476
## [5,] 756 2772 448 672 243 891 144 216 27 99 16 24 2349
## [6,] 728 504 224 252 234 162 72 81 26 18 8 9 2262
## [7,] 364 2380 1736 28 117 765 558 9 13 85 62 1 1131
## [8,] 392 336 1820 2772 126 108 585 891 14 12 65 99 1218
## [9,] 891 3267 528 792 216 792 128 192 1485 5445 880 1320 1836
## [10,] 858 594 264 297 208 144 64 72 1430 990 440 495 1768
## [11,] 429 2805 2046 33 104 680 496 8 715 4675 3410 55 884
## [12,] 462 396 2145 3267 112 96 520 792 770 660 3575 5445 952
## [13,] 1134 4158 672 1008 351 1287 208 312 1647 6039 976 1464 1134
## [14,] 1092 756 336 378 338 234 104 117 1586 1098 488 549 1092
## [15,] 546 3570 2604 42 169 1105 806 13 793 5185 3782 61 546
## [16,] 588 504 2730 4158 182 156 845 1287 854 732 3965 6039 588
## [,14] [,15] [,16]
## [1,] 3366 544 816
## [2,] 612 272 306
## [3,] 2890 2108 34
## [4,] 408 2210 3366
## [5,] 8613 1392 2088
## [6,] 1566 696 783
## [7,] 7395 5394 87
## [8,] 1044 5655 8613
## [9,] 6732 1088 1632
## [10,] 1224 544 612
## [11,] 5780 4216 68
## [12,] 816 4420 6732
## [13,] 4158 672 1008
## [14,] 756 336 378
## [15,] 3570 2604 42
## [16,] 504 2730 4158
#Dr. D has been growing hops to support his craft beer hobby and has established a field of Cascade hops for his favorite Pale Ale. The yields on this patch have been 1.11, 1.46, 1.91, 6.15, 8.43, and 13.82 pounds per year. Following from the example in the lecture, construct a regression of yield as a function of year for these data. Make a plot and describe the components of the basic lm() model textually as you would if you were writing a manuscript.
library(ggplot2)
url <- read.csv("https://docs.google.com/spreadsheets/d/e/2PACX-1vSWwoYeXnxJiD2zAbgKAku-bc5e_J57s3L0GTQL8yuUI_Y7_iBwKtwv0sz1SxsZj28baYBV62-PkdKk/pub?output=csv")
data <- url
ggplot( data, aes(x=Yield, y=Year)) +
stat_smooth( se=FALSE, formula = y~log(x), method="lm" ) +
geom_point( size=2)
# lm is used to fit linear models. It can be used to carry out regression, single stratum analysis of variance and analysis of covariance. lm uses a least squares regression model to estimate the trendline. The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).