213 Midterm S2023
Brandon Nolasco
2023-05-30
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# Define the parameters
population_mean <- 60
population_sd <- 20
sample_size <- 25
num_simulations <- 1000
# Create a vector to store the sample means
sample_means <- numeric(num_simulations)
sample_standard_deviations<-numeric(num_simulations)
# Simulate sampling and calculate sample means
for (i in 1:num_simulations) {
samples <- rnorm(sample_size, population_mean, population_sd)
sample_means[i] <- mean(samples)
sample_standard_deviations[i]<-sd(samples)
}
#sample_means
#sample_standard_deviations
# Calculate the mean, standard deviation, and standard error of the sample means
mean_of_sample_means <- mean(sample_means)
mean_of_sample_standard_deviations<-mean(sample_standard_deviations)
sd_of_sample_means <- sd(sample_means)
se_of_sample_means <- sd_of_sample_means / sqrt(sample_size-1)
SEotE<-sqrt((mean_of_sample_means-population_mean)^2/(sample_size-1))
# Output the results
mean_of_sample_means## [1] 59.96027mean_of_sample_standard_deviations## [1] 19.88741sd_of_sample_means## [1] 4.032389se_of_sample_means## [1] 0.8231079SEotE## [1] 0.008109077Including Plots
You can also embed plots, for example:
library(arm)## Loading required package: MASS## Loading required package: Matrix## Loading required package: lme4##
## arm (Version 1.13-1, built: 2022-8-25)## Working directory is C:/Users/brand/Desktop/UCR/PhD CCN/PSYC213_Spring2023/Lab/Midtermcrash.data<-read.csv("crash.csv")
m1<-lm(Rate~AlcCons+PerMiles,data=crash.data)
m2<-lm(Rate~KillRest+KillUnre+KillRest*KillUnre,data=crash.data)
display(m1)## lm(formula = Rate ~ AlcCons + PerMiles, data = crash.data)
## coef.est coef.se
## (Intercept) -1.64 3.87
## AlcCons -1.93 0.90
## PerMiles 17.96 1.44
## ---
## n = 51, k = 3
## residual sd = 4.38, R-Squared = 0.79display(m2)## lm(formula = Rate ~ KillRest + KillUnre + KillRest * KillUnre,
## data = crash.data)
## coef.est coef.se
## (Intercept) -64.89 33.78
## KillRest 1.36 0.79
## KillUnre 1.27 0.54
## KillRest:KillUnre -0.02 0.01
## ---
## n = 51, k = 4
## residual sd = 8.35, R-Squared = 0.24summary(m1)##
## Call:
## lm(formula = Rate ~ AlcCons + PerMiles, data = crash.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.0272 -2.8275 0.0915 2.7110 12.7452
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.6361 3.8668 -0.423 0.6741
## AlcCons -1.9281 0.9032 -2.135 0.0379 *
## PerMiles 17.9630 1.4376 12.495 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.376 on 48 degrees of freedom
## Multiple R-squared: 0.7869, Adjusted R-squared: 0.778
## F-statistic: 88.61 on 2 and 48 DF, p-value: < 2.2e-16summary(m2)##
## Call:
## lm(formula = Rate ~ KillRest + KillUnre + KillRest * KillUnre,
## data = crash.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.1232 -5.1672 -0.0482 5.2242 17.0232
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -64.88945 33.78050 -1.921 0.0608 .
## KillRest 1.35982 0.79103 1.719 0.0922 .
## KillUnre 1.27468 0.54039 2.359 0.0225 *
## KillRest:KillUnre -0.01521 0.01378 -1.104 0.2753
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.355 on 47 degrees of freedom
## Multiple R-squared: 0.2394, Adjusted R-squared: 0.1908
## F-statistic: 4.93 on 3 and 47 DF, p-value: 0.004655# Load the ggplot2 library
library(ggplot2)
# Create a data frame combining the residuals and fitted values
residualsm1<-residuals(m1)
fitted.values.m1<-fitted.values(m1)
residuals_df <- data.frame(Residuals = residualsm1, Fitted_Values = fitted.values.m1)
# Create a scatter plot of residuals versus fitted values
ggplot(data = residuals_df, aes(x = Fitted_Values, y = Residuals)) +
geom_point() +
labs(x = "Fitted Values", y = "Residuals") +
ggtitle("Residuals versus Fitted Values")
residualsm2<-residuals(m2)
fitted.values.m2<-fitted.values(m2)
residuals_df2 <- data.frame(Residuals = residualsm2, Fitted_Values = fitted.values.m2)
# Create a scatter plot of residuals versus fitted values
ggplot(data = residuals_df2, aes(x = Fitted_Values, y = Residuals)) +
geom_point() +
labs(x = "Fitted Values", y = "Residuals") +
ggtitle("Residuals versus Fitted Values")
AlcCons<-mean(crash.data$AlcCons,na.rm=TRUE)+c(-1,0,1)*sd(crash.data$AlcCons,na.rm=TRUE)
KillUnre<-mean(crash.data$KillUnre,na.rm=TRUE)+c(-1,0,1)*sd(crash.data$KillUnre,na.rm=TRUE)
combs <- expand.grid(AlcCons, KillUnre)
combs## Var1 Var2
## 1 1.933266 47.69781
## 2 2.631176 47.69781
## 3 3.329087 47.69781
## 4 1.933266 56.99412
## 5 2.631176 56.99412
## 6 3.329087 56.99412
## 7 1.933266 66.29043
## 8 2.631176 66.29043
## 9 3.329087 66.29043predict(m1)## 1 2 3 4 5 6 7 8
## 34.199759 29.299236 38.994118 38.312938 19.292685 25.144320 12.724483 21.069702
## 9 10 11 12 13 14 15 16
## 19.703932 32.155983 24.196382 21.532444 31.593663 23.733640 21.162932 30.337230
## 17 18 19 20 21 22 23 24
## 27.053129 32.519146 34.993450 20.372416 19.986798 8.804112 25.742028 18.576118
## 25 26 27 28 29 30 31 32
## 46.503911 27.923944 34.395742 22.708578 28.106994 9.408168 16.355640 34.472865
## 33 34 35 36 37 38 39 40
## 20.391696 28.328843 13.495719 19.308792 25.411079 27.596168 22.804983 10.793219
## 41 42 43 44 45 46 47 48
## 34.858483 31.767191 34.103354 25.626343 25.854539 22.769595 16.837663 16.587011
## 49 50 51
## 34.334725 17.419264 36.384848predict(m2)## 1 2 3 4 5 6 7 8
## 28.94527 23.31288 22.40798 25.49018 20.45396 28.62837 24.67650 29.84510
## 9 10 11 12 13 14 15 16
## 21.02478 28.14584 23.34414 15.57539 28.24756 20.17495 24.62817 22.42529
## 17 18 19 20 21 22 23 24
## 22.95595 30.52749 20.10626 30.15355 24.17188 15.95254 22.81514 18.41057
## 25 26 27 28 29 30 31 32
## 36.30676 26.43972 28.69453 20.58384 24.60661 27.51389 22.21172 27.71945
## 33 34 35 36 37 38 39 40
## 20.37956 19.94188 21.65511 28.91058 34.35016 26.24364 20.03751 32.03320
## 41 42 43 44 45 46 47 48
## 29.53627 25.89958 30.86095 27.83199 25.27377 26.67510 24.83539 27.83655
## 49 50 51
## 29.04444 24.71952 33.48852Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.