Description
There will be two parts to this online assignment. In the first part of this assignment, you will practice applying what we’ve been learning about to a dataset of your choosing. In the second part of this assignment, you will begin performing simulations. We’ll return to the results of the second part of this assignment in a future lecture.
Part 1
- First, select a dataset on a topic that you are interested in. Be sure that the dataset has at least two quantitative variables.
Here are some sources for a dataset to consider:
- Kaggle
- Tidy Tuesday
- Data is Plural
- ICPSR
- UCI Machine Learning Repository
- FiveThirtyEight
- Google’s Dataset Search
If your dataset is located online, provide a link to the dataset. If the dataset is from another source, provide a brief description of the dataset and indicate how you have access to the dataset.
- Load this dataset into R. To do so, download the dataset. Then, place the dataset in the same folder as your .Rmd document. If your data is a .csv file, load it in with code like the following: mydf = read.csv(‘filename.csv’). If your data is a .txt file, load it in with code like the following: mydf = read.delim(‘filename.csv). If your data is in a different format, try searching the internet for sample code, asking in office hours, or posting to campuswire. Once your dataset is in R, print the first few rows of your dataset.
# Use this code chunk for your answer.
setwd(“~/Desktop/data”)
df = read.csv(“MCD64.006.estimates-country-ba.2019_2002-2019.USA_.csv”)
- Provide one critique or area of concern regarding this dataset. Think carefully about the data, and what variables or observations might be missing about the data. How could someone misuse this data?
- Select two quantitative variables from your dataset to further explore. To start, create a scatterplot of these two variables; make sure that your scatterplot is clear and easy to read. Describe the scatterplot.
| # Use this code chunk for your answer.
library(ggplot2) ggplot(data = df, aes(x = ba_ratio_2019…. , y = ba_ratio_2002_2019….)) + geom_point() + labs(title = ‘2019 Burned Area vs. Historical Avg Area Burned – 2002-2019 in North America x = ‘Area Burned in 2019 (% of Country)’, y = ‘Historical Area Burned From 2002-2019 (%)’) + theme_bw() |
‘,
2019 Burned Area vs. Historical Avg Area Burned − 2002−2019 in North Ame
19.
- Generate a linear model to summarize the relationship between your two variables. Write the fitted model and provide an interpretation of your estimated coefficients.
# Use this code chunk for your answer.
lm = lm(ba_ratio_2019…. ~ ba_ratio_2002_2019…., data = df) summary(lm)
##
## Call:
## lm(formula = ba_ratio_2019…. ~ ba_ratio_2002_2019…., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max ## -2.03246 -0.13574 -0.13512 -0.01167 1.46980
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 0.13512 0.10856 1.245 0.221
## ba_ratio_2002_2019…. 0.42143 0.09542 4.417 8.79e-05 *** ## —
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
##
## Residual standard error: 0.5679 on 36 degrees of freedom ## Multiple R-squared: 0.3514, Adjusted R-squared: 0.3334
## F-statistic: 19.51 on 1 and 36 DF, p-value: 8.789e-05
Part 2
We’ll rely on R to help us create “fake” data and then practice understanding a linear model applied to this data.
We’ll provide some initial information to R to set up our data, including our sample size, our x values, and other population characteristics:
sample_size = 21
x_vals = seq(from = 0, to = 10, length.out = sample_size) sigma = 3
- Replace the following code with your birthdate in mmddyyyy form. Currently, the birthday of June 13, 1876, which is William Gosset’s (pen name Student’s) birthday is below.
set.seed(02162001)
- Next, we’ll set some important characteristics for our data. We start by generating the randomness of our data.
epsilon = rnorm(n = sample_size, mean = 0, sd = sigma)
Now, generate the values of y based on the following relationship:
Y = 7 − 1.4x +
where ∼ N(0,σ2 = 9) (independently).
The values of have been generated in the above code chunk. Save the values of y as y_vals in R
# Use this code chunk for your answer. y_vals = 7 – (1.4 * x_vals) + epsilon
- Uncomment the following line of code to create a data frame that contains both x and y.
sim_data = data.frame(x_vals, y_vals)
Report the dimensions of this data frame. Print the first few rows of this data frame. Calculate the correlation between x & y.
# Use this code chunk for your answer.
dim(sim_data)
## [1] 21 2
head(sim_data)
## x_vals y_vals ## 1 0.0 10.792018 ## 2 0.5 8.284465 ## 3 1.0 7.798642 ## 4 1.5 11.060227 ## 5 2.0 3.846448 ## 6 2.5 -2.172807
cor(sim_data$x_vals, sim_data$y_vals)
## [1] -0.8234135
- Create a linear model that predicts y from our x values. Print the summary values for this model. What are the fitted coefficients? Make sure to type the fitted coefficients below. Do they seem reasonable based on our true relationship printed above?
# Use this code chunk for your answer.
lm1 = lm(y_vals ~ x_vals) summary(lm1)
##
## Call:
## lm(formula = y_vals ~ x_vals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7471 -2.0222 0.1536 1.7195 5.2466
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.2378 1.3542 6.083 7.53e-06 *** ## x_vals -1.4654 0.2317 -6.325 4.53e-06 ***
## —
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
##
## Residual standard error: 3.214 on 19 degrees of freedom
## Multiple R-squared: 0.678, Adjusted R-squared: 0.6611
## F-statistic: 40.01 on 1 and 19 DF, p-value: 4.533e-06
- Write out the fitted model. Based on this fitted model, what is yˆ when x = 2 and when x = 12. Which (if either) of these values do you trust more? Why?
# Use this code chunk for your answer.
x_2 = 8.2378 + (2 * -1.4654) x_2
## [1] 5.307
x_12 = 8.2378 + (12 * -1.4654) x_12
## [1] -9.347
summary(x_vals)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 2.5 5.0 5.0 7.5 10.0
