# Load necessary package and data
library(readr)
display_data <- read_csv("Display_data.csv")## Rows: 29 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (8): spend, clicks, impressions, display, transactions, revenue, ctr, co...
##
## 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.head(display_data)## # A tibble: 6 × 8
## spend clicks impressions display transactions revenue ctr con_rate
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 22.6 165 8672 0 2 58.9 1.9 1.21
## 2 37.3 228 11875 0 2 44.9 1.92 0.88
## 3 55.6 291 14631 0 3 142. 1.99 1.03
## 4 45.4 247 11709 0 2 210. 2.11 0.81
## 5 50.2 290 14768 0 3 198. 1.96 1.03
## 6 33.0 172 8698 0 2 204. 1.98 1.16H₀=Advertising spend has no effect on revenue. H₁=Advertising spend has a significant effect on revenue.
# Simple Linear Regression Model: revenue ~ spend
model_simple <- lm(revenue ~ spend, data = display_data)
summary(model_simple)##
## Call:
## lm(formula = revenue ~ spend, data = display_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -145.210 -54.647 1.117 67.780 149.476
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.9397 37.9668 0.288 0.775
## spend 4.8066 0.7775 6.182 1.31e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 86.71 on 27 degrees of freedom
## Multiple R-squared: 0.586, Adjusted R-squared: 0.5707
## F-statistic: 38.22 on 1 and 27 DF, p-value: 1.311e-06R²: 0.586: About 59% of the variation in revenue is from spend alone.
Coefficient: 4.81, p is less than 0.001 and so it is statistically significant
Interpretation: For every $1 increase in spend, revenue increases by about $4.81
Managerial Recommendation: Since there is a strong positive/significant relationship between spend and revenue, they should increase the ad spending and it should, in turn, increase the revenue.
H₀: Display and spend have no effect on revenue H₁: Display and/or spend significantly affect revenue
# Multiple Linear Regression Model: revenue ~ spend + display
model_multiple <- lm(revenue ~ spend + display, data = display_data)
summary(model_multiple)##
## Call:
## lm(formula = revenue ~ spend + display, data = display_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -176.730 -35.020 8.661 56.440 129.231
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -50.8612 40.3336 -1.261 0.21850
## spend 5.5473 0.7415 7.482 6.07e-08 ***
## display 93.5856 33.1910 2.820 0.00908 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 77.33 on 26 degrees of freedom
## Multiple R-squared: 0.6829, Adjusted R-squared: 0.6586
## F-statistic: 28 on 2 and 26 DF, p-value: 3.271e-07R squared:0.683, Model improves with Display added, roughly 68% of revenue variation explained
Spend Coefficient = 5.55, p is less than 0.001
Display Coefficient = 93.59, p = 0.009 which is also significant
Managerial Recommendations: Since display ads and spending both significantly boost revenue, the company should run more ads while also increasing the spending budget for the two.