Math 2305 Data Science Assignment
Instruction
Save this file as “Math_2305_data_science_assignment_your_first_name_last_name.Rmd” (e.g., assignment4_jonny_appleseed.Rmd).
For each task, provide appropriate R command(s) in the code chunk, and execute the code chunk to generate an outcome.
After completing all tasks, save the your Rmd file, and produce an HTML report. 3a. Make sure to delete all intermediate code chunks before creating an HTML report.
Submit your Rmd file and the rendered HTML report to D2L by its due date.
1. Load the data file (5 points)
- Load
Math 2305 Data Science Assignment_data.csvand save it in an R object so that you can use in the subsequent analysis. Usetidyversepackage in this RMD file as you will use data science tools and techniques when analyzing the data.
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.4.2## Warning: package 'ggplot2' was built under R version 4.4.2## Warning: package 'tibble' was built under R version 4.4.2## Warning: package 'tidyr' was built under R version 4.4.2## Warning: package 'readr' was built under R version 4.4.2## Warning: package 'purrr' was built under R version 4.4.2## Warning: package 'dplyr' was built under R version 4.4.2## Warning: package 'stringr' was built under R version 4.4.2## Warning: package 'forcats' was built under R version 4.4.2## Warning: package 'lubridate' was built under R version 4.4.2## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdf <- read_csv("dsacities.csv")## Rows: 77 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): county, district, grspan
## dbl (14): distcod, teachers, calwpct, mealpct, computer, testscr, compstu, e...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.dfExamine the loaded data set
2. How many rows and columns does it have? (3 points)
dim(df)## [1] 77 173. Examine the first several rows of the data sets (3 points)
head(df)4. Compute mean and standard deviation of teachers,
compstu, and testscr values (4 point)
df2 <- df %>%
summarize(mean_teachers = mean(teachers),
sd_teachers = sd(teachers),
mean_compstu = mean(compstu),
sd_compstu = sd(compstu),
mean_testscr = mean(testscr),
sd_testscr = sd(testscr))
df25. Create a scatter plot of readscr
vs. mathscr (5 point)
- Use
readscrfor the X axis - Use “Reading score” for the X axis label
- Use
mathscrfor the Y axis - Use “Math score” for the Y axis label
- Show a best fit line
df %>%
ggplot(aes(x = readscr, y = mathscr)) +
geom_point() +
geom_smooth(method = "lm") +
labs(x = "Reading score", y = "Math score", title = "Reading versus Math")## `geom_smooth()` using formula = 'y ~ x'
6. Compute a correlation between readscr and
mathscr (30 points)
- State null hypothesis and alternative hypothesis
My Response:
Ho:There is a linear correlation between ‘readscr’ and ‘mathscr’.
Ha:There is a positive correlation between “readscr’ and ‘mathscr’.
- Report the test statistics, degree of freedom and statistical significance
My Response:
The t-statistic for the observed correlation is approximately t
=21.843. In addition, the test has 75 degrees of freedom. Furthermore,
regarding the statistical significance, the p - value is extremely
small, approximately 2.2e-16. Given this p-value, there’s compelling
evidence against the null hypothesis of no correlation, leading us to
reject Ho, which states there no linear correlation between reading and
math scores. This suggests that the observed strong positive correlation
between readscr and mathscr is statistically
significant and is not a result of random variations in our sample.
- Describe the meaning of p-value in words
My Response:
The p-value tells us the probability that the observed relationship
between readscr and mathscr could have
happened due to random occurrences in the dataset. A small p-value (like
less than 0.05) suggests that the observed relationship has statistical
significance; this means that we can reasonably generalize this
relationship to the broader population, implying it’s not just a result
of random occurrences in our sample.
cor.test(df$readscr, df$mathscr)##
## Pearson's product-moment correlation
##
## data: df$readscr and df$mathscr
## t = 21.843, df = 75, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8911715 0.9547822
## sample estimates:
## cor
## 0.92959917. Report the findings from your correlation analysis (30 points)
- Write a sentence describing the findings
- Make sure to include all important information
My Response:
From our analysis, the test statistic is t = 21.843 with a degree of freedom of 75, and a p -value of 2.2e-16. Given we are using a 95% confidence interval, our significance level (alpha) is 0.05. Since the p-value is greater than alpha, we accept the null hypothesis (Ho) not in favor of the alternative hypothesis (Ha). As mentioned, this suggests a statistivally significant positive linear relationship between reading and math scores (r = 0.9295991, p = 2.2e-16 > .05)
8. Create an HTML report of your correlation analysis
Note: Professor reserves the right to decide what answers, code, and step-processs is correct not the student. Once the student submits the assignment, they are not able to resubmit for a higher grade and all grades are final when the professor inserts them in D2L.
Convert to HTML for 20 points and submit both the markdown file (.rmd) and HTML to the assignment folder in D2L.
You will have a total of 100 points for this assignment.