Lab 6

1. Load the dataset

1. Load the dataset covid_data_states.csv from Canvas (Files/Labs). Use the function read_cvs (different from read.csv) to read the data into a tibble. Assign a name to the imported dataset (e.g. data). You can check the definition of each variable here.

covid_data <- read.csv("covid_data_states.csv")
view(covid_data)

2. Get to know the data

Describe the dataset: The data set goes into detail labels state, country, population, positivity ratio, case density, infection rate & more information on the Covid-19 virus.

1. What is the unit of observation, i.e. what does each row correspond to? How many observations are there? The unit of observation is humans/population.The first unit of observation is “country”, there are 52 units of observation.

ncol(covid_data)

## [1] 52

2. Define new variables containing new cases per capita, deaths per capita, and vaccinations per capita. Add them to the original dataset.

covid_data$tests_per_capita <- covid_data$actuals.positiveTests / covid_data$population
covid_data$deaths_per_capita <- covid_data$actuals.deaths / covid_data$population
covid_data$vaccinations_per_capita <- covid_data$actuals.vaccinesDistributed / covid_data$population

3. Use the skim function from the skimr package to obtain common summary statistics for the variables new cases per capita, deaths per capita, and vaccinations per capita. (Hint: Use dplyr to select the variables and then simple pipe (%>%) skim().)

summary_stats <- covid_data %>%
  select(tests_per_capita, deaths_per_capita, vaccinations_per_capita) %>%
  skim()

4. Do you have any priors about the actual (linear) relationship between deaths per capita and vaccinations per capita? What would you do to get a first insight?

I do have priors, I would assume that the more vaccinations per capita would decrese the deaths per capita. To ge a first insight I would use common sense to get a general understanding of what the data should look like and do some research on the topic.

5. Compute the correlation between deaths and vaccinations per capita? Is the relationship positive/negative, strong/weak? Do the same for the non-per-capita version of the variables. The relationship is positive but also weak, vaccinations reduce deaths. For non-per-capita the data shows more deaths for the more vaccinations.

ggplot(covid_data, aes(x = vaccinations_per_capita, y = deaths_per_capita)) +
  geom_point() +
  xlab("Vaccinations per capita") +
  ylab("Deaths per capita")

ggplot(covid_data, aes(x = actuals.vaccinesDistributed, y = actuals.deaths)) +
  geom_point() +
  xlab("Vaccinations") +
  ylab("Deaths")

3. Regression.

1. Run the following regression: \(deaths\; per\; capita = b_0+b_1vaccination\;rate + e_i\). After running the regression, answer the questions below.

regression <- lm(deaths_per_capita ~ vaccinations_per_capita, data = covid_data)

summary(regression)

## 
## Call:
## lm(formula = deaths_per_capita ~ vaccinations_per_capita, data = covid_data)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0015679 -0.0004479  0.0001212  0.0003763  0.0014222 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              0.0031076  0.0008504   3.654 0.000609 ***
## vaccinations_per_capita -0.0010184  0.0006382  -1.596 0.116727    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0006721 on 51 degrees of freedom
## Multiple R-squared:  0.04755,    Adjusted R-squared:  0.02888 
## F-statistic: 2.546 on 1 and 51 DF,  p-value: 0.1167

2. Are coefficients similar to those found in class? Do they differ in a way that makes sense? The coefficients are similar to those that were shown in class.

3. What is the predicted change in deaths when moving from 0.3 vaccination rate to 0.8?

You can assume that increasing the vaccination rate would decrease the deaths.

regression_model <- lm(deaths_per_capita ~ vaccinations_per_capita, data = covid_data)

b0 <- coef(regression_model)[1]
b1 <- coef(regression_model)[2]

deaths_per_capita_0_3 <- b0 + b1 * 0.3
deaths_per_capita_0_8 <- b0 + b1 * 0.8

delta_deaths_per_capita <- deaths_per_capita_0_8 - deaths_per_capita_0_3
delta_deaths_per_capita

##   (Intercept) 
## -0.0005092128

4. Show that the sum of residuals is zero (save the regression object and look at residuals. You can take a very small number as a zero.

residuals <- residuals(regression_model)
sum_of_residuals <- sum(residuals)
sum_of_residuals

## [1] -5.854692e-18