M03-2: Data Visualization-Application Assignment

#install.packages("ggplot2")
#install.packages("gt")
library(tidyverse)
library(ggrepel)
library(ggthemes)
library(scales)
library(plotly)
library(lattice)
library(GGally)

# install this package:
install.packages("wooldridge")

Error in `contrib.url()`:
! trying to use CRAN without setting a mirror

library(wooldridge)
help(attend)
df <- attend
head(df)

  attend termGPA priGPA ACT final atndrte hwrte frosh soph missed     stndfnl
1     27    3.19   2.64  23    28  84.375 100.0     0    1      5  0.47268906
2     22    2.73   3.52  25    26  68.750  87.5     0    0     10  0.05252101
3     30    3.00   2.46  24    30  93.750  87.5     0    0      2  0.89285713
4     31    2.04   2.61  20    27  96.875 100.0     0    1      1  0.26260504
5     32    3.68   3.32  23    34 100.000 100.0     0    1      0  1.73319328
6     29    3.23   2.93  26    25  90.625 100.0     0    1      3 -0.15756303

class(df)

[1] "data.frame"

df <- as_tibble(df)
df

# A tibble: 680 × 11
   attend termGPA priGPA   ACT final atndrte hwrte frosh  soph missed stndfnl
    <int>   <dbl>  <dbl> <int> <int>   <dbl> <dbl> <int> <int>  <int>   <dbl>
 1     27    3.19   2.64    23    28    84.4 100       0     1      5  0.473 
 2     22    2.73   3.52    25    26    68.8  87.5     0     0     10  0.0525
 3     30    3      2.46    24    30    93.8  87.5     0     0      2  0.893 
 4     31    2.04   2.61    20    27    96.9 100       0     1      1  0.263 
 5     32    3.68   3.32    23    34   100   100       0     1      0  1.73  
 6     29    3.23   2.93    26    25    90.6 100       0     1      3 -0.158 
 7     30    1.54   1.94    21    10    93.8  75       1     0      2 -3.31  
 8     26    2      2.12    22    34    81.2 100       0     1      6  1.73  
 9     24    2.25   2.06    24    26    75   100       1     0      8  0.0525
10     29    3      2.73    21    26    90.6 100       0     1      3  0.0525
# ℹ 670 more rows

Variable Definition - attend: classes attended out of 32 - termGPA: GPA for term - priGPA: cumulative GPA prior to term - ACT: ACT score - final: final exam score - atndrte: percent classes attended - hwrte: percent homework turned in - frosh: =1 if freshman - soph: =1 if sophomore - missed: number of classes missed - stndfnl: (final - mean)/sd

1 Ex 1: GT table

# install.packages(c("wooldridge","gt","dplyr"))  # if needed
library(wooldridge)
library(dplyr)

library(gt)
data("attend")

# A clean, presentable summary table using gt
attend %>%
  select(attend, termGPA, priGPA, ACT, final, atndrte, hwrte, frosh, soph, missed, stndfnl) %>%
  summarise(
    across(
      everything(),
      list(
        N = ~sum(!is.na(.)),
        Mean = ~mean(., na.rm = TRUE),
        SD = ~sd(., na.rm = TRUE),
        Min = ~min(., na.rm = TRUE),
        Max = ~max(., na.rm = TRUE)
      )
    )
  ) %>%
  tidyr::pivot_longer(
    cols = everything(),
    names_to = c("Variable", ".value"),
    names_sep = "_"
  ) %>%
  gt() %>%
  tab_header(
    title = "Wooldridge Dataset: attend",
    subtitle = "Descriptive statistics for key variables"
  ) %>%
  cols_label(
    Variable = "Variable",
    N = "N",
    Mean = "Mean",
    SD = "Std Dev",
    Min = "Min",
    Max = "Max"
  ) %>%
  fmt_number(
    columns = c(Mean, SD, Min, Max),
    decimals = 2
  ) %>%
  tab_style(
    style = cell_text(weight = "bold"),
    locations = cells_column_labels(everything())
  ) %>%
  tab_options(
    table.font.size = px(14),
    heading.title.font.size = px(20),
    heading.subtitle.font.size = px(14),
    table.width = pct(90)
  ) %>%
  data_color(
    columns = Mean,
    method = "numeric",
    palette = c("#e8f5e9", "#66bb6a", "#1b5e20")
  ) %>%
  tab_source_note(
    source_note = "Source: wooldridge::attend"
  )

Wooldridge Dataset: attend
Descriptive statistics for key variables
Variable	N	Mean	Std Dev	Min	Max
attend	680	26.15	5.46	2.00	32.00
termGPA	680	2.60	0.74	0.00	4.00
priGPA	680	2.59	0.54	0.86	3.93
ACT	680	22.51	3.49	13.00	32.00
final	680	25.89	4.71	10.00	39.00
atndrte	680	81.71	17.05	6.25	100.00
hwrte	674	87.91	19.27	12.50	100.00
frosh	680	0.23	0.42	0.00	1.00
soph	680	0.58	0.49	0.00	1.00
missed	680	5.85	5.46	0.00	30.00
stndfnl	680	0.03	0.99	−3.31	2.78
Source: wooldridge::attend

2 Ex2: Scatter plot with ggplot2

# install.packages(c("wooldridge","ggplot2","dplyr"))  # if needed
library(wooldridge)
library(ggplot2)
library(dplyr)

data("attend")
df <- attend  # since your prompt says variables are inside df

# (Optional) Make soph readable for faceting/caption
df <- df %>%
  mutate(
    soph_f = factor(soph, levels = c(0, 1),
                    labels = c("Not Sophomore (0)", "Sophomore (1)"))
  )

# 2.1 + 2.2 + 2.3 (and a bit extra polish)
ggplot(df, aes(x = priGPA, y = missed)) +
  geom_point(size = 2, color = "blue", alpha = 0.65) +         # points: size=2, blue
  geom_smooth(method = "lm", se = TRUE, color = "red") +       # regression line: red
  facet_wrap(~ soph_f) +                                       # facet by soph
  theme_bw() +                                                 # theme bw
  labs(
    title = "Prior GPA vs. Missed Classes (Faceted by Sophomore Status)",
    x = "Prior (Cumulative) GPA (priGPA)",
    y = "Number of Classes Missed (missed)",
    caption = "Moderator: soph (0 = Not Sophomore, 1 = Sophomore)"
  )

3 Ex 3: Understand barplots (dodge vs. stack vs. faceted)

library(wooldridge)
library(ggplot2)
library(dplyr)

data("attend")
df <- attend %>%
  mutate(
    soph_f = factor(soph, levels = c(0, 1),
                    labels = c("Not Sophomore (0)", "Sophomore (1)"))
  )

# 3.1 Barplot: count of ACT scores
p31 <- ggplot(df, aes(x = ACT)) +
  geom_bar() +
  theme_bw() +
  labs(
    title = "Count of ACT Scores",
    x = "ACT score",
    y = "Count"
  )
p31

# For 3.2, ACT must be treated as categorical to make a bar chart by ACT level
df2 <- df %>% mutate(ACT_f = factor(ACT))

# --- 3.2 (A) Dodged bar chart (y = mean(final) by ACT, filled by soph)
p_dodge <- ggplot(df2, aes(x = ACT_f, y = final, fill = soph_f)) +
  stat_summary(fun = mean, geom = "bar", position = "dodge") +
  theme_bw() +
  labs(
    title = "Mean Final Exam Score by ACT (Dodged) — by Sophomore Status",
    x = "ACT score",
    y = "Mean final exam score",
    fill = "Soph status"
  )
p_dodge

# --- 3.2 (B) Stacked bar chart (same summary, stacked)
p_stack <- ggplot(df2, aes(x = ACT_f, y = final, fill = soph_f)) +
  stat_summary(fun = mean, geom = "bar", position = "stack") +
  theme_bw() +
  labs(
    title = "Mean Final Exam Score by ACT (Stacked) — by Sophomore Status",
    x = "ACT score",
    y = "Mean final exam score (stacked across groups)",
    fill = "Soph status"
  )
p_stack

# --- 3.2 (C) Faceted bar chart (mean(final) by ACT in separate panels)
p_facet <- ggplot(df2, aes(x = ACT_f, y = final)) +
  stat_summary(fun = mean, geom = "bar") +
  facet_wrap(~ soph_f) +
  theme_bw() +
  labs(
    title = "Mean Final Exam Score by ACT (Faceted) — by Sophomore Status",
    x = "ACT score",
    y = "Mean final exam score"
  )
p_facet

3.1 3.2 What distribution does ACT count resemble?

A bar plot of ACT values often looks roughly bell-shaped (approximately normal): most students cluster around a middle ACT range, with fewer observations at very low/high ACT scores. (It won’t be perfectly smooth because ACT is discrete and sample sizes vary.)

3.2 3.3 Which chart “accurately” describes the data, and why?

• Most accurate: Dodged or faceted
  • They let you compare mean (final) between sophomore groups with the same ACT score without mixing groups.
• Least appropriate: Stacked
  • Stacking can be misleading because stacking implies “parts of a whole”
  • The stack height becomes the mean of group A + the mean of groups B which is not a meaningful quantity for final exam scores

4 Ex 4: Barplots with ACT averages (Understand Bar plots)

library(wooldridge)
library(dplyr)
library(ggplot2)

data("attend")

# Relabel soph (same idea as earlier)
df_soph_relabeled <- attend %>%
  mutate(
    soph_f = factor(soph, levels = c(0, 1),
                    labels = c("Not Sophomore (0)", "Sophomore (1)"))
  )

# 4.1 Summarize: average final by soph and ACT + sample size
df_soph_relabeled_summarized <- df_soph_relabeled %>%
  group_by(soph_f, ACT) %>%
  summarise(
    final_avg = mean(final, na.rm = TRUE),
    n = n(),
    .groups = "drop"
  ) %>%
  mutate(ACT_f = factor(ACT))  # treat ACT as categorical for bar charts

df_soph_relabeled_summarized

# A tibble: 38 × 5
   soph_f              ACT final_avg     n ACT_f
   <fct>             <int>     <dbl> <int> <fct>
 1 Not Sophomore (0)    14      20       1 14   
 2 Not Sophomore (0)    15      24.3     6 15   
 3 Not Sophomore (0)    16      24.2    11 16   
 4 Not Sophomore (0)    17      25.2    13 17   
 5 Not Sophomore (0)    18      25      14 18   
 6 Not Sophomore (0)    19      23.3    23 19   
 7 Not Sophomore (0)    20      25.6    30 20   
 8 Not Sophomore (0)    21      23.2    29 21   
 9 Not Sophomore (0)    22      25.5    28 22   
10 Not Sophomore (0)    23      26.0    38 23   
# ℹ 28 more rows

# --- 4.1 (A) Dodged bar chart (y = final_avg)
p4_dodge <- ggplot(df_soph_relabeled_summarized,
                   aes(x = ACT_f, y = final_avg, fill = soph_f)) +
  geom_col(position = "dodge") +
  theme_bw() +
  labs(
    title = "Average Final Exam Score by ACT (Dodged) — by Sophomore Status",
    x = "ACT score",
    y = "Average final exam score",
    fill = "Soph status"
  )
p4_dodge

# --- 4.1 (B) Stacked bar chart (y = final_avg)  [shown because prompt asks, but see notes in 4.2]
p4_stack <- ggplot(df_soph_relabeled_summarized,
                   aes(x = ACT_f, y = final_avg, fill = soph_f)) +
  geom_col(position = "stack") +
  theme_bw() +
  labs(
    title = "Average Final Exam Score by ACT (Stacked) — by Sophomore Status",
    x = "ACT score",
    y = "Average final exam score (stacked across groups)",
    fill = "Soph status"
  )
p4_stack

# --- 4.1 (C) Faceted bar chart (y = final_avg)
p4_facet <- ggplot(df_soph_relabeled_summarized,
                   aes(x = ACT_f, y = final_avg)) +
  geom_col() +
  facet_wrap(~ soph_f) +
  theme_bw() +
  labs(
    title = "Average Final Exam Score by ACT (Faceted) — by Sophomore Status",
    x = "ACT score",
    y = "Average final exam score"
  )
p4_facet

4.1 Which charts accurately describe the data? Why?

• faceted/dodged
  • shows average final score for each ACT level sperately for each sophmore group which matches the meaning of final_avg
• Not accurate / misleading: Stacked
  • Stacking averages creates a bar height that equals avg(non-soph) + avg(soph), which is not a meaningful statistic for exam scores (it suggests “parts of a whole,” but averages are not parts).

4.2 Q3.2 dodged vs Q4 dodged: which would you trust?

Trust the Q4 dodged chart (the one using final_avg after summarizing). Why: - In Q3, if you used final directly in a bar, ggplot has to aggregate somehow (and beginners often end up with something that looks like a mean but they didn’t explicitly compute it). - In Q4, you explicitly compute the mean by group_by(soph, ACT) then plot final_avg. That’s transparent, reproducible, and you can also inspect n.

4.3 Differences in patterns between soph and non-soph

What to look for: - If both groups’ averages rise with ACT, you’ll say: higher ACT is associated with higher average final scores for both groups.

• If one group’s curve/bars increase more strongly (bigger slope across ACT), you’ll say: the ACT–final relationship is stronger for that group (evidence of moderation)

• If the groups are consistently separated (one always higher at each ACT), you’ll say: group difference in final performance across ACT levels (a main effect of soph group).

• If at high/low ACT the bars jump around and the n labels are small, mention: some ACT levels have small sample sizes, so those averages are less stable.

5 Ex 5: Boxplot vs. correct barplot

library(wooldridge)
library(dplyr)
library(ggplot2)

data("attend")

df <- attend %>%
  mutate(
    soph_f = factor(soph, levels = c(0, 1),
                    labels = c("Not Sophomore (0)", "Sophomore (1)")),
    ACT_f = factor(ACT)   # treat ACT as categorical for boxplots
  )

ggplot(df, aes(x = ACT_f, y = final, fill = soph_f)) +
  geom_boxplot(alpha = 0.5, outlier.alpha = 0.3, position = position_dodge(width = 0.8)) +
  geom_jitter(
    aes(color = soph_f),
    position = position_jitterdodge(jitter.width = 0.15, dodge.width = 0.8),
    alpha = 0.35,
    size = 1.5
  ) +
  theme_bw() +
  labs(
    title = "Final Exam Score by ACT Score (Boxplot + Jittered Points)",
    subtitle = "Grouped by sophomore status",
    x = "ACT score",
    y = "Final exam score",
    fill = "Soph status",
    color = "Soph status",
    caption = "Box = median/IQR; points show individual students (jittered)."
  )

5.1 5.2 Box plot vs. “correct” bar plot (from Q4) + which I prefer

The barplot (Q4) summarizes each ACT × soph group with a single average final score, which is simple for comparing central tendency but hides what’s happening inside each group. Your boxplot (Q5) shows the median and spread (IQR) of final scores at each ACT score, plus the jittered points reveal sample density and outliers. In your figure, many ACT levels have noticeable spread (often several points wide) and a few unusually low or high scores—details that would be invisible in a mean-only bar chart.

I prefer the boxplot + jitter because it shows both the typical score (median) and variability/outliers, making it easier to judge whether apparent differences between groups are meaningful or just due to noisy/small-sample ACT levels. The barplot is still useful as a quick “average trend” summary, but the boxplot is more informative and less likely to oversimplify.

5.2 5.3 Differences in ACT–final patterns for soph vs non-soph (what your plot suggests)

Your plot shows a clear positive relationship between ACT and final exam score for both groups: as ACT increases from the mid-teens into the high 20s/low 30s, the boxes and medians shift upward, indicating higher typical final scores at higher ACT levels.

Comparing groups, the Sophomore (1) and Not Sophomore (0) distributions overlap heavily at most ACT scores, and the medians are usually close—so sophomore status doesn’t look like it creates a huge difference in final scores once ACT is considered. If anything, at some higher ACT values the sophomore group’s median looks slightly higher, but the overlap is still substantial.

Finally, variability is non-trivial at many ACT levels (wide boxes and scattered points), meaning that students with the same ACT can still have quite different final scores. This is another reason the boxplot is helpful: it shows that ACT predicts higher performance on average, but there’s still plenty of spread within each ACT group.

6 Ex 6: Impact of ACT on attednace, moderated by freshman status: Boxplot

library(wooldridge)
library(dplyr)
library(ggplot2)

data("attend")

df <- attend %>%
  mutate(
    ACT_f   = factor(ACT),  # make ACT discrete for boxplot x-axis
    frosh_f = factor(frosh, levels = c(0, 1),
                     labels = c("Not Freshman (0)", "Freshman (1)"))
  )

# (A) One chart: grouped boxplots (side-by-side) + jittered points
ggplot(df, aes(x = ACT_f, y = attend, fill = frosh_f)) +
  geom_boxplot(alpha = 0.5, position = position_dodge(width = 0.8),
               outlier.alpha = 0.25) +
  geom_jitter(
    aes(color = frosh_f),
    position = position_jitterdodge(jitter.width = 0.15, dodge.width = 0.8),
    alpha = 0.30, size = 1.3
  ) +
  theme_bw() +
  labs(
    title = "Classes Attended by ACT Score (Boxplot + Jittered Points)",
    subtitle = "Grouped by freshman status",
    x = "ACT score",
    y = "Classes attended (out of 32)",
    fill = "Freshman status",
    color = "Freshman status",
    caption = "Box = median/IQR; points are individual students (jittered)."
  )

# (B) Two charts: facet by freshman status (often easier to compare patterns)
ggplot(df, aes(x = ACT_f, y = attend)) +
  geom_boxplot(alpha = 0.6, outlier.alpha = 0.25) +
  geom_jitter(alpha = 0.30, width = 0.15, size = 1.3) +
  facet_wrap(~ frosh_f) +
  theme_bw() +
  labs(
    title = "Classes Attended by ACT Score (Faceted Boxplots)",
    subtitle = "One panel per freshman status",
    x = "ACT score",
    y = "Classes attended (out of 32)"
)

6.0.1 What the plots show

• Not Freshman (0): Attendance is generally high across most ACT scores (medians clustered around the high-20s out of 32), but there’s more spread at many ACT values and quite a few low-attendance outliers (some students missing a lot of classes) spread throughout the ACT range.

• Freshman (1): The medians are also fairly high, but the panel looks noisier with fewer points at some ACT scores (suggesting smaller sample sizes). There are still some low-attendance outliers, and the variability seems to jump more from ACT to ACT.

6.0.2 6.2 Is the relationship the same for non-freshmen vs freshmen?

Not exactly. In both groups, there isn’t a strong “higher ACT leads higher attendance” pattern (attendance stays relatively high across ACT levels), so ACT doesn’t look like a strong driver of attendance overall. However, the non-freshman group shows a more stable pattern (more consistent medians and lots of data), while the freshman group looks more variable/noisy and appears more affected by small-sample ACT levels. So freshman status seems to moderate the relationship mainly by changing variability/stability, not by flipping the direction of the relationship.

7 Ex 7: Attendancce by ACT, moderated by freshman status: Scatter Plot

library(wooldridge)
library(dplyr)
library(ggplot2)

data("attend")

df <- attend %>%
  mutate(
    frosh_f = factor(frosh, levels = c(0, 1),
                     labels = c("Not Freshman (0)", "Freshman (1)"))
  )

# (A) One chart: both groups together + separate regression lines
ggplot(df, aes(x = ACT, y = attend, color = frosh_f)) +
  geom_point(alpha = 0.45, size = 2) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_bw() +
  labs(
    title = "Attendance by ACT Score (Scatter + Regression Line)",
    subtitle = "Colored by freshman status",
    x = "ACT score",
    y = "Classes attended (out of 32)",
    color = "Freshman status",
    caption = "Lines are OLS fits within each freshman group."
  )

# (B) Two charts: facet by freshman status (often clearer)
ggplot(df, aes(x = ACT, y = attend)) +
  geom_point(alpha = 0.45, size = 2) +
  geom_smooth(method = "lm", se = TRUE, color = "red") +
  facet_wrap(~ frosh_f) +
  theme_bw() +
  labs(
    title = "Attendance by ACT Score (Faceted Scatter + Regression Line)",
    subtitle = "One panel per freshman status",
    x = "ACT score",
    y = "Classes attended (out of 32)",
    caption = "Red line is an OLS fit within each panel."
  )

7.1 Do group differences become clear or obscure with the scatter + fitted line?

They become clearer. The scatterplot makes it obvious that the ACT attendance relationship is negative in both groups (downward red lines), and it also makes the difference in slopes between groups easier to see than in bar/box plots. At the same time, the scatter shows a lot of variability (many points clustered near high attendance with some low-attendance outliers), which explains why the relationship isn’t “tight” even though the trend is visible.

7.2 Summary of the relationship + how it differs by freshman status

• Overall relationship: In both panels, the fitted line slopes downward, suggesting that higher ACT scores are associated with slightly lower class attendance (fewer classes attended out of 32).

• Moderation (difference across groups): The downward slope is stronger for Freshmen (1) than for Not Freshmen (0). In other words, ACT appears to be more negatively related to attendance among freshmen.

• Variability/outliers: Both groups show substantial spread, including some students with very low attendance across a range of ACT scores. The clustering near the top (around ~28–32 attended) plus outliers suggests ACT alone doesn’t explain attendance very well, even though the negative trend exists.

8 Ex 8: Correlations

library(wooldridge)
library(GGally)
library(dplyr)
library(ggplot2)

data("attend")

vars <- c("attend","termGPA","priGPA","ACT","final","atndrte","hwrte")

df_cor <- attend %>%
  select(all_of(vars)) %>%
  na.omit()

# ---- 8.1 (A) ggpairs: scatterplots + correlations
ggpairs(
  df_cor,
  upper = list(continuous = wrap("cor", size = 4)),
  lower = list(continuous = wrap("points", alpha = 0.5, size = 1.2)),
  diag  = list(continuous = "densityDiag")
) +
  theme_bw()

# ---- 8.1 (B) ggcorr: correlation heatmap
ggcorr(
  df_cor,
  method = c("pairwise", "pearson"),
  label = TRUE,
  label_size = 3
) +
  theme_bw() +
  labs(title = "Correlation Heatmap (Pearson r)")

# ---- 8.2 Find the highest positive correlation pair + next highest
C <- cor(df_cor, use = "pairwise.complete.obs")

# zero out diagonal + lower triangle so we only search unique pairs
C_upper <- C
C_upper[lower.tri(C_upper, diag = TRUE)] <- NA

# sort correlations high -> low
pairs_sorted <- sort(C_upper, decreasing = TRUE, na.last = NA)

# top pair
top_r <- pairs_sorted[1]
top_idx <- which(C_upper == top_r, arr.ind = TRUE)[1,]
top_pair <- c(rownames(C_upper)[top_idx[1]], colnames(C_upper)[top_idx[2]])

cat("Highest positive correlation:\n",
    top_pair[1], "and", top_pair[2], "with r =", round(top_r, 3), "\n\n")

Highest positive correlation:
 attend and atndrte with r = 1 

# next few highest (you can change 5 to however many you want)
cat("Next highest correlations:\n")

Next highest correlations:

print(round(pairs_sorted[2:6], 3))

[1] 0.654 0.626 0.626 0.538 0.538

8.1 ggpairs() vs ggcorr(): which do I like and why

• ggcorr() (heatmap) is great for a quick scan of which relationships are strongest/weakest.

• ggpairs() is more informative because it shows the scatterplots + distributions, so you can see outliers, ceiling effects, and nonlinearity that a single correlation number can hide.

• I prefer ggpairs() here because several variables (like attendance measures) have ceiling clustering and visible structure in the scatterplots, and ggpairs() makes that easier to interpret.

8.2 Highest positive correlation + next highest

8.2.1 Highest positive correlation

• attend and atndrte: r = 1.000

  This makes perfect sense because atndrte is basically attend expressed as a percentage (same information, different scale).

8.2.2 Next highest correlations (after that)

• termGPA and priGPA: r = 0.654

  Makes sense: students who had higher GPA before the term tend to also earn higher GPA during the term.

• attend and hwrte: r = 0.626

Other fairly strong ones you have:

• termGPA & atndrte: r = 0.538

• attend & termGPA: r = 0.538

• termGPA & final: r = 0.522

• termGPA & hwrte: r = 0.505

8.3 8.3 Attendance rate vs homework rate: which looks more effective for improving GPA?

Eyeballing correlations with GPA outcomes:

With term GPA

termGPA vs atndrte: r = 0.538

• termGPA vs hwrte: r = 0.505

• Attendance rate (atndrte) is slightly more strongly associated with term GPA.

With pri GPA

• priGPA vs atndrte: r = 0.420

• priGPA vs hwrte: r = 0.307

• attendance rate (atndrte) shows a clearly stronger association.

Conclusion: Based on your correlation results, attendance rate (atndrte) looks like the more effective lever (stronger correlation with both termGPA and priGPA)—with the usual reminder that correlation ≠ causation.

9 Ex 9: Scatter plot with regression line for the Impact of priGPA on termGPA

library(wooldridge)
library(dplyr)
library(ggplot2)

data("attend")

df <- attend %>%
  mutate(
    soph_f = factor(soph, levels = c(0, 1),
                    labels = c("Not Sophomore (0)", "Sophomore (1)"))
  )

plot <- ggplot(df, aes(x = priGPA, y = termGPA, color = soph_f)) +
  geom_point(alpha = 0.55, size = 2) +
  geom_smooth(method = "lm", se = TRUE) +
  theme_bw() +
  labs(
    title = "termGPA vs priGPA (Separate OLS Lines by Sophomore Status)",
    x = "Prior GPA (priGPA)",
    y = "Term GPA (termGPA)",
    color = "Soph status",
    caption = "Lines are linear regression fits within each soph group."
  )

plot  # print the chart

9.1 9.2 What can you say about the strength of priGPA–termGPA relationship?

From your earlier correlation matrix, termGPA and priGPA have a fairly strong positive correlation (~0.654), so you should expect:

• A clear positive linear trend: higher priGPA generally predicts higher termGPA.

• The relationship is moderately strong (not perfect): you’ll still see scatter around the lines because term GPA also depends on course difficulty, effort this term, attendance/homework, etc.

• When you split by soph, you’ll likely see two very similar upward lines unless the interaction term shows a meaningful difference—so sophomore status may shift the line slightly (level) and/or slightly change the slope (moderation).

10 Ex 10: Interactive Plot & Save the plot from EX 9.

# install.packages("plotly")  # if needed
library(plotly)

# If your Ex9 plot used df with soph_f, make sure df still exists.
# Add hover labels (shows soph + priGPA + termGPA)
plot_labeled <- plot +
  aes(text = paste0(
    "soph: ", soph,               # or use soph_f if you prefer labels
    "<br>priGPA: ", round(priGPA, 2),
    "<br>termGPA: ", round(termGPA, 2)
  ))

plot_labeled <- plot + aes(text = paste0("soph: ", soph_f,
                                        "<br>priGPA: ", round(priGPA,2),
                                        "<br>termGPA: ", round(termGPA,2)))
ggplotly(plot_labeled, tooltip = "text")

ggsave("myplot.png", plot = plot, width = 8, height = 5, dpi = 300)

10.1 Github Education Application