ADEC 7320 Discussion 2
Yuqi
2023-09-11
Part I.
#First dataset "airquality"
#load the datasets
library(datasets)
airquality## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6
## 7 23 299 8.6 65 5 7
## 8 19 99 13.8 59 5 8
## 9 8 19 20.1 61 5 9
## 10 NA 194 8.6 69 5 10
## 11 7 NA 6.9 74 5 11
## 12 16 256 9.7 69 5 12
## 13 11 290 9.2 66 5 13
## 14 14 274 10.9 68 5 14
## 15 18 65 13.2 58 5 15
## 16 14 334 11.5 64 5 16
## 17 34 307 12.0 66 5 17
## 18 6 78 18.4 57 5 18
## 19 30 322 11.5 68 5 19
## 20 11 44 9.7 62 5 20
## 21 1 8 9.7 59 5 21
## 22 11 320 16.6 73 5 22
## 23 4 25 9.7 61 5 23
## 24 32 92 12.0 61 5 24
## 25 NA 66 16.6 57 5 25
## 26 NA 266 14.9 58 5 26
## 27 NA NA 8.0 57 5 27
## 28 23 13 12.0 67 5 28
## 29 45 252 14.9 81 5 29
## 30 115 223 5.7 79 5 30
## 31 37 279 7.4 76 5 31
## 32 NA 286 8.6 78 6 1
## 33 NA 287 9.7 74 6 2
## 34 NA 242 16.1 67 6 3
## 35 NA 186 9.2 84 6 4
## 36 NA 220 8.6 85 6 5
## 37 NA 264 14.3 79 6 6
## 38 29 127 9.7 82 6 7
## 39 NA 273 6.9 87 6 8
## 40 71 291 13.8 90 6 9
## 41 39 323 11.5 87 6 10
## 42 NA 259 10.9 93 6 11
## 43 NA 250 9.2 92 6 12
## 44 23 148 8.0 82 6 13
## 45 NA 332 13.8 80 6 14
## 46 NA 322 11.5 79 6 15
## 47 21 191 14.9 77 6 16
## 48 37 284 20.7 72 6 17
## 49 20 37 9.2 65 6 18
## 50 12 120 11.5 73 6 19
## 51 13 137 10.3 76 6 20
## 52 NA 150 6.3 77 6 21
## 53 NA 59 1.7 76 6 22
## 54 NA 91 4.6 76 6 23
## 55 NA 250 6.3 76 6 24
## 56 NA 135 8.0 75 6 25
## 57 NA 127 8.0 78 6 26
## 58 NA 47 10.3 73 6 27
## 59 NA 98 11.5 80 6 28
## 60 NA 31 14.9 77 6 29
## 61 NA 138 8.0 83 6 30
## 62 135 269 4.1 84 7 1
## 63 49 248 9.2 85 7 2
## 64 32 236 9.2 81 7 3
## 65 NA 101 10.9 84 7 4
## 66 64 175 4.6 83 7 5
## 67 40 314 10.9 83 7 6
## 68 77 276 5.1 88 7 7
## 69 97 267 6.3 92 7 8
## 70 97 272 5.7 92 7 9
## 71 85 175 7.4 89 7 10
## 72 NA 139 8.6 82 7 11
## 73 10 264 14.3 73 7 12
## 74 27 175 14.9 81 7 13
## 75 NA 291 14.9 91 7 14
## 76 7 48 14.3 80 7 15
## 77 48 260 6.9 81 7 16
## 78 35 274 10.3 82 7 17
## 79 61 285 6.3 84 7 18
## 80 79 187 5.1 87 7 19
## 81 63 220 11.5 85 7 20
## 82 16 7 6.9 74 7 21
## 83 NA 258 9.7 81 7 22
## 84 NA 295 11.5 82 7 23
## 85 80 294 8.6 86 7 24
## 86 108 223 8.0 85 7 25
## 87 20 81 8.6 82 7 26
## 88 52 82 12.0 86 7 27
## 89 82 213 7.4 88 7 28
## 90 50 275 7.4 86 7 29
## 91 64 253 7.4 83 7 30
## 92 59 254 9.2 81 7 31
## 93 39 83 6.9 81 8 1
## 94 9 24 13.8 81 8 2
## 95 16 77 7.4 82 8 3
## 96 78 NA 6.9 86 8 4
## 97 35 NA 7.4 85 8 5
## 98 66 NA 4.6 87 8 6
## 99 122 255 4.0 89 8 7
## 100 89 229 10.3 90 8 8
## 101 110 207 8.0 90 8 9
## 102 NA 222 8.6 92 8 10
## 103 NA 137 11.5 86 8 11
## 104 44 192 11.5 86 8 12
## 105 28 273 11.5 82 8 13
## 106 65 157 9.7 80 8 14
## 107 NA 64 11.5 79 8 15
## 108 22 71 10.3 77 8 16
## 109 59 51 6.3 79 8 17
## 110 23 115 7.4 76 8 18
## 111 31 244 10.9 78 8 19
## 112 44 190 10.3 78 8 20
## 113 21 259 15.5 77 8 21
## 114 9 36 14.3 72 8 22
## 115 NA 255 12.6 75 8 23
## 116 45 212 9.7 79 8 24
## 117 168 238 3.4 81 8 25
## 118 73 215 8.0 86 8 26
## 119 NA 153 5.7 88 8 27
## 120 76 203 9.7 97 8 28
## 121 118 225 2.3 94 8 29
## 122 84 237 6.3 96 8 30
## 123 85 188 6.3 94 8 31
## 124 96 167 6.9 91 9 1
## 125 78 197 5.1 92 9 2
## 126 73 183 2.8 93 9 3
## 127 91 189 4.6 93 9 4
## 128 47 95 7.4 87 9 5
## 129 32 92 15.5 84 9 6
## 130 20 252 10.9 80 9 7
## 131 23 220 10.3 78 9 8
## 132 21 230 10.9 75 9 9
## 133 24 259 9.7 73 9 10
## 134 44 236 14.9 81 9 11
## 135 21 259 15.5 76 9 12
## 136 28 238 6.3 77 9 13
## 137 9 24 10.9 71 9 14
## 138 13 112 11.5 71 9 15
## 139 46 237 6.9 78 9 16
## 140 18 224 13.8 67 9 17
## 141 13 27 10.3 76 9 18
## 142 24 238 10.3 68 9 19
## 143 16 201 8.0 82 9 20
## 144 13 238 12.6 64 9 21
## 145 23 14 9.2 71 9 22
## 146 36 139 10.3 81 9 23
## 147 7 49 10.3 69 9 24
## 148 14 20 16.6 63 9 25
## 149 30 193 6.9 70 9 26
## 150 NA 145 13.2 77 9 27
## 151 14 191 14.3 75 9 28
## 152 18 131 8.0 76 9 29
## 153 20 223 11.5 68 9 30#Second dateset
chickwts## weight feed
## 1 179 horsebean
## 2 160 horsebean
## 3 136 horsebean
## 4 227 horsebean
## 5 217 horsebean
## 6 168 horsebean
## 7 108 horsebean
## 8 124 horsebean
## 9 143 horsebean
## 10 140 horsebean
## 11 309 linseed
## 12 229 linseed
## 13 181 linseed
## 14 141 linseed
## 15 260 linseed
## 16 203 linseed
## 17 148 linseed
## 18 169 linseed
## 19 213 linseed
## 20 257 linseed
## 21 244 linseed
## 22 271 linseed
## 23 243 soybean
## 24 230 soybean
## 25 248 soybean
## 26 327 soybean
## 27 329 soybean
## 28 250 soybean
## 29 193 soybean
## 30 271 soybean
## 31 316 soybean
## 32 267 soybean
## 33 199 soybean
## 34 171 soybean
## 35 158 soybean
## 36 248 soybean
## 37 423 sunflower
## 38 340 sunflower
## 39 392 sunflower
## 40 339 sunflower
## 41 341 sunflower
## 42 226 sunflower
## 43 320 sunflower
## 44 295 sunflower
## 45 334 sunflower
## 46 322 sunflower
## 47 297 sunflower
## 48 318 sunflower
## 49 325 meatmeal
## 50 257 meatmeal
## 51 303 meatmeal
## 52 315 meatmeal
## 53 380 meatmeal
## 54 153 meatmeal
## 55 263 meatmeal
## 56 242 meatmeal
## 57 206 meatmeal
## 58 344 meatmeal
## 59 258 meatmeal
## 60 368 casein
## 61 390 casein
## 62 379 casein
## 63 260 casein
## 64 404 casein
## 65 318 casein
## 66 352 casein
## 67 359 casein
## 68 216 casein
## 69 222 casein
## 70 283 casein
## 71 332 caseinDescription of Datasets
1. Airquality
This dataset records daily air quality measurements in New York, May to September 1973. Furthermore, this dataset contains 153 observations(m=153) and 6 variables(n=6).
#get more information about the dataset
help(airquality)Ozone: numeric Ozone (ppb)
Solar. R: numeric Solar R (lang)
Wind: numeric Wind (mph)
Temp: numeric Temperature (degrees F)
Month: numeric Month( 1-12)
Day: numeric Day of month (1-31)
#check the structure of airquality
str(airquality)## 'data.frame': 153 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 NA 28 23 19 8 NA ...
## $ Solar.R: int 190 118 149 313 NA NA 299 99 19 194 ...
## $ Wind : num 7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
## $ Temp : int 67 72 74 62 56 66 65 59 61 69 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 5 6 7 8 9 10 ...#check the missing values of airquality
Ozone_na <- any(is.na(airquality$Ozone))
Ozone_na## [1] TRUESolar.R_na <- any(is.na(airquality$Solar.R))
Solar.R_na ## [1] TRUEWind_na <- any(is.na(airquality$Wind))
Wind_na ## [1] FALSETemp_na <- any(is.na(airquality$Temp))
Temp_na## [1] FALSEMonth_na <- any(is.na(airquality$Month))
Month_na## [1] FALSEDay_na <- any(is.na(airquality$Day))
Day_na## [1] FALSEBased on the findings, both Ozone and Solar.R have missing values. This highlights the need to implement techniques to handle these missing values for further analysis.
#check the summary statistics for each variable
summary(airquality$Ozone)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 1.00 18.00 31.50 42.13 63.25 168.00 37summary(airquality$Solar.R)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 7.0 115.8 205.0 185.9 258.8 334.0 7summary(airquality$Wind)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.700 7.400 9.700 9.958 11.500 20.700summary(airquality$Temp)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 56.00 72.00 79.00 77.88 85.00 97.00#install.packages("TSstudio", dependencies=TRUE)
#install.packages("tidyverse")
library(TSstudio)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.0 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.3 ✔ tibble 3.1.8
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors# Add a Date column to the airquality dataset
airquality$Date <- as.Date(with(airquality, paste(1973, Month, Day, sep="-")), "%Y-%m-%d")
# Plot the Ozone time series
ts_plot(airquality[,c("Date", "Ozone")], title = "Ozone Levels Over Time")# Plot the Solar.R time series
ts_plot(airquality[, c("Date", "Solar.R")], title = "Solar.R Levels Over Time")#Plot the Wind time series
ts_plot(airquality[, c("Date", "Wind")], title = "Wind Levels Over Time")#Plot the Temp time series
ts_plot(airquality[, c("Date", "Temp")], title = "Temp Levels Over Time")Conclusion:
Based on the graphs, airquality is a time series dataset. As the description in both ’Month” and ’Day” columns indicates sequential dates from May to September with daily observations.
2. Chickwts
This dataset with 71 observations and 2 variables. To be more specific, it capture the weights of chicken fed with different types of feed after six weeks.
#get more information about chickwts
help(chickwts)weight: A numeric variable giving the chick weight
feed: a factor giving the feed type
#check the structure of airquality
str(chickwts)## 'data.frame': 71 obs. of 2 variables:
## $ weight: num 179 160 136 227 217 168 108 124 143 140 ...
## $ feed : Factor w/ 6 levels "casein","horsebean",..: 2 2 2 2 2 2 2 2 2 2 ...#No missing value
any(is.na(chickwts))## [1] FALSE#Check the unique feed types and their counts
table(chickwts$feed)##
## casein horsebean linseed meatmeal soybean sunflower
## 12 10 12 11 14 12#compute summary statistics for each feed type
summary_stats <- chickwts %>%
group_by(feed) %>%
summarise(
count = n(),
mean_weight = mean(weight),
median_weight = median(weight),
min_weight = min(weight),
max_weight = max(weight),
sd_weight = sd(weight)
)
print(summary_stats)## # A tibble: 6 × 7
## feed count mean_weight median_weight min_weight max_weight sd_weight
## <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 casein 12 324. 342 216 404 64.4
## 2 horsebean 10 160. 152. 108 227 38.6
## 3 linseed 12 219. 221 141 309 52.2
## 4 meatmeal 11 277. 263 153 380 64.9
## 5 soybean 14 246. 248 158 329 54.1
## 6 sunflower 12 329. 328 226 423 48.8ggplot(chickwts, aes(x=weight)) +
geom_histogram(binwidth=10, fill="skyblue", color="black", alpha=0.7) +
facet_wrap(~feed) +
theme_light() +
labs(title="Histogram of Chicken Weights by Different Feed Type",
y="Frequency",
x="Weight") 
Conclusion:
The ‘chickwts’ dataset capture the snapshot of weights at a specific point of time (after 6 week). Thus, this dataset can be considered as a cross - sectional dataset.
Part II.
1.
Covariance measures changes in x variable are associated with changes in y variable. To be more specific, if the covariance between x and y is positive which indicates the value of x increases, the values of y will increase. Thus, covariance qualify the relationship between two variables.
Variance measures the dispersion of data values around their mean. A large value of variance indicates a wide spread in the dataset, meaning the data points are scattered farther from the mean.
The general idea of the slope of a linear regression indicates the average change. Covariance measures the joint variability if y and x, and variance measures how much x changes. By taking the ratio, we get the average change in y for each unit change in x.
Show in R
airquality## Ozone Solar.R Wind Temp Month Day Date ## 1 41 190 7.4 67 5 1 1973-05-01 ## 2 36 118 8.0 72 5 2 1973-05-02 ## 3 12 149 12.6 74 5 3 1973-05-03 ## 4 18 313 11.5 62 5 4 1973-05-04 ## 5 NA NA 14.3 56 5 5 1973-05-05 ## 6 28 NA 14.9 66 5 6 1973-05-06 ## 7 23 299 8.6 65 5 7 1973-05-07 ## 8 19 99 13.8 59 5 8 1973-05-08 ## 9 8 19 20.1 61 5 9 1973-05-09 ## 10 NA 194 8.6 69 5 10 1973-05-10 ## 11 7 NA 6.9 74 5 11 1973-05-11 ## 12 16 256 9.7 69 5 12 1973-05-12 ## 13 11 290 9.2 66 5 13 1973-05-13 ## 14 14 274 10.9 68 5 14 1973-05-14 ## 15 18 65 13.2 58 5 15 1973-05-15 ## 16 14 334 11.5 64 5 16 1973-05-16 ## 17 34 307 12.0 66 5 17 1973-05-17 ## 18 6 78 18.4 57 5 18 1973-05-18 ## 19 30 322 11.5 68 5 19 1973-05-19 ## 20 11 44 9.7 62 5 20 1973-05-20 ## 21 1 8 9.7 59 5 21 1973-05-21 ## 22 11 320 16.6 73 5 22 1973-05-22 ## 23 4 25 9.7 61 5 23 1973-05-23 ## 24 32 92 12.0 61 5 24 1973-05-24 ## 25 NA 66 16.6 57 5 25 1973-05-25 ## 26 NA 266 14.9 58 5 26 1973-05-26 ## 27 NA NA 8.0 57 5 27 1973-05-27 ## 28 23 13 12.0 67 5 28 1973-05-28 ## 29 45 252 14.9 81 5 29 1973-05-29 ## 30 115 223 5.7 79 5 30 1973-05-30 ## 31 37 279 7.4 76 5 31 1973-05-31 ## 32 NA 286 8.6 78 6 1 1973-06-01 ## 33 NA 287 9.7 74 6 2 1973-06-02 ## 34 NA 242 16.1 67 6 3 1973-06-03 ## 35 NA 186 9.2 84 6 4 1973-06-04 ## 36 NA 220 8.6 85 6 5 1973-06-05 ## 37 NA 264 14.3 79 6 6 1973-06-06 ## 38 29 127 9.7 82 6 7 1973-06-07 ## 39 NA 273 6.9 87 6 8 1973-06-08 ## 40 71 291 13.8 90 6 9 1973-06-09 ## 41 39 323 11.5 87 6 10 1973-06-10 ## 42 NA 259 10.9 93 6 11 1973-06-11 ## 43 NA 250 9.2 92 6 12 1973-06-12 ## 44 23 148 8.0 82 6 13 1973-06-13 ## 45 NA 332 13.8 80 6 14 1973-06-14 ## 46 NA 322 11.5 79 6 15 1973-06-15 ## 47 21 191 14.9 77 6 16 1973-06-16 ## 48 37 284 20.7 72 6 17 1973-06-17 ## 49 20 37 9.2 65 6 18 1973-06-18 ## 50 12 120 11.5 73 6 19 1973-06-19 ## 51 13 137 10.3 76 6 20 1973-06-20 ## 52 NA 150 6.3 77 6 21 1973-06-21 ## 53 NA 59 1.7 76 6 22 1973-06-22 ## 54 NA 91 4.6 76 6 23 1973-06-23 ## 55 NA 250 6.3 76 6 24 1973-06-24 ## 56 NA 135 8.0 75 6 25 1973-06-25 ## 57 NA 127 8.0 78 6 26 1973-06-26 ## 58 NA 47 10.3 73 6 27 1973-06-27 ## 59 NA 98 11.5 80 6 28 1973-06-28 ## 60 NA 31 14.9 77 6 29 1973-06-29 ## 61 NA 138 8.0 83 6 30 1973-06-30 ## 62 135 269 4.1 84 7 1 1973-07-01 ## 63 49 248 9.2 85 7 2 1973-07-02 ## 64 32 236 9.2 81 7 3 1973-07-03 ## 65 NA 101 10.9 84 7 4 1973-07-04 ## 66 64 175 4.6 83 7 5 1973-07-05 ## 67 40 314 10.9 83 7 6 1973-07-06 ## 68 77 276 5.1 88 7 7 1973-07-07 ## 69 97 267 6.3 92 7 8 1973-07-08 ## 70 97 272 5.7 92 7 9 1973-07-09 ## 71 85 175 7.4 89 7 10 1973-07-10 ## 72 NA 139 8.6 82 7 11 1973-07-11 ## 73 10 264 14.3 73 7 12 1973-07-12 ## 74 27 175 14.9 81 7 13 1973-07-13 ## 75 NA 291 14.9 91 7 14 1973-07-14 ## 76 7 48 14.3 80 7 15 1973-07-15 ## 77 48 260 6.9 81 7 16 1973-07-16 ## 78 35 274 10.3 82 7 17 1973-07-17 ## 79 61 285 6.3 84 7 18 1973-07-18 ## 80 79 187 5.1 87 7 19 1973-07-19 ## 81 63 220 11.5 85 7 20 1973-07-20 ## 82 16 7 6.9 74 7 21 1973-07-21 ## 83 NA 258 9.7 81 7 22 1973-07-22 ## 84 NA 295 11.5 82 7 23 1973-07-23 ## 85 80 294 8.6 86 7 24 1973-07-24 ## 86 108 223 8.0 85 7 25 1973-07-25 ## 87 20 81 8.6 82 7 26 1973-07-26 ## 88 52 82 12.0 86 7 27 1973-07-27 ## 89 82 213 7.4 88 7 28 1973-07-28 ## 90 50 275 7.4 86 7 29 1973-07-29 ## 91 64 253 7.4 83 7 30 1973-07-30 ## 92 59 254 9.2 81 7 31 1973-07-31 ## 93 39 83 6.9 81 8 1 1973-08-01 ## 94 9 24 13.8 81 8 2 1973-08-02 ## 95 16 77 7.4 82 8 3 1973-08-03 ## 96 78 NA 6.9 86 8 4 1973-08-04 ## 97 35 NA 7.4 85 8 5 1973-08-05 ## 98 66 NA 4.6 87 8 6 1973-08-06 ## 99 122 255 4.0 89 8 7 1973-08-07 ## 100 89 229 10.3 90 8 8 1973-08-08 ## 101 110 207 8.0 90 8 9 1973-08-09 ## 102 NA 222 8.6 92 8 10 1973-08-10 ## 103 NA 137 11.5 86 8 11 1973-08-11 ## 104 44 192 11.5 86 8 12 1973-08-12 ## 105 28 273 11.5 82 8 13 1973-08-13 ## 106 65 157 9.7 80 8 14 1973-08-14 ## 107 NA 64 11.5 79 8 15 1973-08-15 ## 108 22 71 10.3 77 8 16 1973-08-16 ## 109 59 51 6.3 79 8 17 1973-08-17 ## 110 23 115 7.4 76 8 18 1973-08-18 ## 111 31 244 10.9 78 8 19 1973-08-19 ## 112 44 190 10.3 78 8 20 1973-08-20 ## 113 21 259 15.5 77 8 21 1973-08-21 ## 114 9 36 14.3 72 8 22 1973-08-22 ## 115 NA 255 12.6 75 8 23 1973-08-23 ## 116 45 212 9.7 79 8 24 1973-08-24 ## 117 168 238 3.4 81 8 25 1973-08-25 ## 118 73 215 8.0 86 8 26 1973-08-26 ## 119 NA 153 5.7 88 8 27 1973-08-27 ## 120 76 203 9.7 97 8 28 1973-08-28 ## 121 118 225 2.3 94 8 29 1973-08-29 ## 122 84 237 6.3 96 8 30 1973-08-30 ## 123 85 188 6.3 94 8 31 1973-08-31 ## 124 96 167 6.9 91 9 1 1973-09-01 ## 125 78 197 5.1 92 9 2 1973-09-02 ## 126 73 183 2.8 93 9 3 1973-09-03 ## 127 91 189 4.6 93 9 4 1973-09-04 ## 128 47 95 7.4 87 9 5 1973-09-05 ## 129 32 92 15.5 84 9 6 1973-09-06 ## 130 20 252 10.9 80 9 7 1973-09-07 ## 131 23 220 10.3 78 9 8 1973-09-08 ## 132 21 230 10.9 75 9 9 1973-09-09 ## 133 24 259 9.7 73 9 10 1973-09-10 ## 134 44 236 14.9 81 9 11 1973-09-11 ## 135 21 259 15.5 76 9 12 1973-09-12 ## 136 28 238 6.3 77 9 13 1973-09-13 ## 137 9 24 10.9 71 9 14 1973-09-14 ## 138 13 112 11.5 71 9 15 1973-09-15 ## 139 46 237 6.9 78 9 16 1973-09-16 ## 140 18 224 13.8 67 9 17 1973-09-17 ## 141 13 27 10.3 76 9 18 1973-09-18 ## 142 24 238 10.3 68 9 19 1973-09-19 ## 143 16 201 8.0 82 9 20 1973-09-20 ## 144 13 238 12.6 64 9 21 1973-09-21 ## 145 23 14 9.2 71 9 22 1973-09-22 ## 146 36 139 10.3 81 9 23 1973-09-23 ## 147 7 49 10.3 69 9 24 1973-09-24 ## 148 14 20 16.6 63 9 25 1973-09-25 ## 149 30 193 6.9 70 9 26 1973-09-26 ## 150 NA 145 13.2 77 9 27 1973-09-27 ## 151 14 191 14.3 75 9 28 1973-09-28 ## 152 18 131 8.0 76 9 29 1973-09-29 ## 153 20 223 11.5 68 9 30 1973-09-30lm(data = airquality, Temp ~ Wind )## ## Call: ## lm(formula = Temp ~ Wind, data = airquality) ## ## Coefficients: ## (Intercept) Wind ## 90.13 -1.23cov(airquality$Temp, airquality$Wind)/var(airquality$Wind)## [1] -1.230479