• We analyze the impact of advertising budgets on sales.
• Data includes advertising spending on TV, Radio, and Newspaper.

• The dataset contains sales figures and advertising budgets
• Source: https://www.statlearning.com/s/Advertising.csv

# load libraries
library(knitr)
library(ggplot2)
library(plotly)

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

knitr::opts_chunk$set(echo = TRUE, fig.width = 10, fig.height = 6, out.width = "100%", out.height = "100%")
# load dataset
data <- read.csv('https://www.statlearning.com/s/Advertising.csv')
head(data)

##   X    TV radio newspaper sales
## 1 1 230.1  37.8      69.2  22.1
## 2 2  44.5  39.3      45.1  10.4
## 3 3  17.2  45.9      69.3   9.3
## 4 4 151.5  41.3      58.5  18.5
## 5 5 180.8  10.8      58.4  12.9
## 6 6   8.7  48.9      75.0   7.2

• Visualizing the relationships between variables.

# scatter plots
ggplot(data, aes(x=TV, y=sales)) + geom_point() + ggtitle("sales vs TV advertising") + theme_minimal()

ggplot(data, aes(x=radio, y=sales)) + geom_point() + ggtitle("sales vs radio Advertising") + theme_minimal()

ggplot(data, aes(x=newspaper, y=sales)) + geom_point() + ggtitle("sales vs newspaper Advertising") + theme_minimal()

• Fit a linear model to predict sales based on TV advertising.

# linear model
model <- lm(sales ~ TV, data=data)
summary(model)

## 
## Call:
## lm(formula = sales ~ TV, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.3860 -1.9545 -0.1913  2.0671  7.2124 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 7.032594   0.457843   15.36   <2e-16 ***
## TV          0.047537   0.002691   17.67   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.259 on 198 degrees of freedom
## Multiple R-squared:  0.6119, Adjusted R-squared:  0.6099 
## F-statistic: 312.1 on 1 and 198 DF,  p-value: < 2.2e-16

• assessing model performance.

# regression line
p <- ggplot(data, aes(x=TV, y=sales)) + geom_point() + geom_smooth(method="lm", col="blue") + ggtitle("Linear Regression: sales vs TV") +theme_minimal()
ggplotly(p) %>% layout(autosize = TRUE)

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

\[ \hat{Y} = \beta_0 + \beta_1 \cdot X \] - Intercept (\(\beta_0\)): 7.0326 - Slope (\(\beta_1\)): 0.0475

p <- ggplot(data, aes(x=TV, y=sales)) + geom_point() + geom_smooth(method="lm", col="blue") + ggtitle("linear regression: sales vs TV") + theme_minimal()
ggplotly(p) %>% layout(autosize = TRUE)

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

• TV advertising has a significant positive effect on sales.
• Further analysis would include multiple regression with all advertising options(tv, radio, newspaper)