Bivariate Analysis: Lincoln Financial vs John Hancock

library(tidyverse)
library(readr)
library(ggplot2)

---

1. Load and clean Google Trends CSV

# Load the file, skipping the first two lines that contain metadata
raw <- read_csv("multiTimeline.csv", skip = 2, show_col_types = FALSE)

# Rename columns for easier use
trends <- raw |>
  rename(
    Date = 1,
    Lincoln_Financial_Index = 2,
    John_Hancock_Index = 3
  )

# Convert Date to date format
trends <- trends |>
  mutate(Date = as.Date(Date))

# Quick look at cleaned data
glimpse(trends)

## Rows: 262
## Columns: 3
## $ Date                    <date> 2020-10-25, 2020-11-01, 2020-11-08, 2020-11-1…
## $ Lincoln_Financial_Index <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ John_Hancock_Index      <dbl> 51, 49, 58, 58, 54, 59, 60, 61, 48, 61, 71, 66…

head(trends)

## # A tibble: 6 × 3
##   Date       Lincoln_Financial_Index John_Hancock_Index
##   <date>                       <dbl>              <dbl>
## 1 2020-10-25                       0                 51
## 2 2020-11-01                       0                 49
## 3 2020-11-08                       0                 58
## 4 2020-11-15                       0                 58
## 5 2020-11-22                       0                 54
## 6 2020-11-29                       0                 59

---

2. (scatterplot + regression line)

ggplot(trends, aes(x = Lincoln_Financial_Index, y = John_Hancock_Index)) +
  geom_point(alpha = 0.7, color = "#0072B2") +
  geom_smooth(method = "lm", se = TRUE, color = "#D55E00") +
  labs(
    title = "Lincoln Financial vs John Hancock (Google Trends)",
    x = "Lincoln Financial (Index 0–100)",
    y = "John Hancock (Index 0–100)"
  ) +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'

---

3. Correlation coefficient

cor_val <- cor(trends$Lincoln_Financial_Index,
               trends$John_Hancock_Index,
               use = "complete.obs")
cor_val

## [1] 0.549074

Interpretation: - r ≈ 1: Strong positive relationship
- r ≈ 0: No relationship
- r ≈ −1: Strong negative relationship

---

4. Simple linear regression

Model: \[ \text{John Hancock} = \beta_0 + \beta_1(\text{Lincoln Financial}) + \varepsilon \]

model <- lm(John_Hancock_Index ~ Lincoln_Financial_Index, data = trends)
summary(model)

## 
## Call:
## lm(formula = John_Hancock_Index ~ Lincoln_Financial_Index, data = trends)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -34.383  -4.335  -0.335   3.445  30.665 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             58.33478    0.74785   78.00   <2e-16 ***
## Lincoln_Financial_Index  0.13643    0.01288   10.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.659 on 260 degrees of freedom
## Multiple R-squared:  0.3015, Adjusted R-squared:  0.2988 
## F-statistic: 112.2 on 1 and 260 DF,  p-value: < 2.2e-16

---

5. Visualize regression with R²

r2_val <- summary(model)$r.squared
ggplot(trends, aes(Lincoln_Financial_Index, John_Hancock_Index)) +
  geom_point(alpha = 0.7) +
  geom_smooth(method = "lm", se = FALSE, color = "#D55E00") +
  annotate("text", x = 10, y = 90, label = paste("R² =", round(r2_val, 3)), hjust = 0) +
  labs(title = "Regression: John Hancock ~ Lincoln Financial",
       x = "Lincoln Financial (Index)",
       y = "John Hancock (Index)") +
  theme_minimal()

## `geom_smooth()` using formula = 'y ~ x'