Regression
Kristen Sosulski
12/10/2018
1. Import and view the data
library(readxl)
ad <- read_excel("ad.xlsx")
knitr::kable(head(ad, 14),booktabs = TRUE)| State | AdEx | Sales |
|---|---|---|
| NJ | 5.0 | 432.0 |
| NY | 7.0 | 723.0 |
| AK | 6.0 | 578.0 |
| HI | 6.5 | 600.0 |
| FL | 8.0 | 950.0 |
| CA | 3.5 | 106.0 |
| OR | 4.0 | 282.0 |
| WA | 4.5 | 232.6 |
| NV | 6.5 | 746.0 |
| AZ | 7.0 | 812.4 |
| CO | 7.5 | 800.0 |
| CT | 7.5 | 929.0 |
| DE | 8.5 | 1004.0 |
| SC | 7.0 | 632.0 |
2. Visualize the data as a scatter plot
library(ggplot2)
scatter01 <- ggplot(ad, aes(x=AdEx, y=Sales)) + geom_point(color='#4cbea3') + labs(title = "Simple scatter plot", subtitle = "Sales (in 1000's of dollars)", caption = "Kristen Sosulski | Source: Rohit Deo (2018)", x = "Advertising expenditures", y =" ") + theme(text=element_text(family="Avenir")) + theme_bw() + theme(panel.border = element_blank(), panel.grid.major = element_blank(), panel.grid.minor = element_blank(), axis.line = element_line(colour = "gray"), axis.ticks.x=element_blank(), axis.ticks.y=element_blank())
scatter01
3. Visualize the regression plot
scatter01 + geom_smooth(method = "lm", se = FALSE, color="gray")
4. The regression equation
The regression equation is Sales = -495 + 178 AdEx
linearMod <- lm(Sales ~ AdEx, data=ad)
print(linearMod)##
## Call:
## lm(formula = Sales ~ AdEx, data = ad)
##
## Coefficients:
## (Intercept) AdEx
## -495.3 178.1summary(linearMod)##
## Call:
## lm(formula = Sales ~ AdEx, data = ad)
##
## Residuals:
## Min 1Q Median 3Q Max
## -119.346 -37.380 -4.869 54.998 88.609
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -495.28 77.06 -6.427 3.27e-05 ***
## AdEx 178.09 11.87 15.000 3.89e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 65.36 on 12 degrees of freedom
## Multiple R-squared: 0.9494, Adjusted R-squared: 0.9451
## F-statistic: 225 on 1 and 12 DF, p-value: 3.888e-09