The objective of this tutorial is to explain how bivariate analysis works.This analysis can be used by marketers to make decisions about their pricing strategies, advertising strategies, and promotion strategies among others.
Bivariate analysis is one of the simplest forms of statistical analysis. It is generally used to find out if there is a relationship between two sets of values (or two variables). That said, it usually involves the variables X and Y (statisticshowto.com).
https://www.qualtrics.com/experience-management/research/research-design/
plot(y3 ~ x3, data = anscombe, pch = 16)
abline(lm(y3 ~ x3, anscombe), col = "grey20")
fit <- lm(y3 ~ x3, anscombe)
summary(fit)
##
## Call:
## lm(formula = y3 ~ x3, data = anscombe)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1586 -0.6146 -0.2303 0.1540 3.2411
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.0025 1.1245 2.670 0.02562 *
## x3 0.4997 0.1179 4.239 0.00218 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.236 on 9 degrees of freedom
## Multiple R-squared: 0.6663, Adjusted R-squared: 0.6292
## F-statistic: 17.97 on 1 and 9 DF, p-value: 0.002176
library(readr)
library(readr)
ad_sales <- read_csv('https://raw.githubusercontent.com/utjimmyx/regression/master/advertising.csv')
## New names:
## Rows: 200 Columns: 6
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," dbl
## (6): ...1, X1, TV, radio, newspaper, sales
## 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.
## • `` -> `...1`
plot(sales ~ TV, data = ad_sales)
fit <- lm(sales ~ TV, data = ad_sales)
summary(fit)
##
## Call:
## lm(formula = sales ~ TV, data = ad_sales)
##
## 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
library(readr)
library(readr)
ad_sales <- read_csv('https://raw.githubusercontent.com/utjimmyx/regression/master/advertising.csv')
## New names:
## Rows: 200 Columns: 6
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," dbl
## (6): ...1, X1, TV, radio, newspaper, sales
## 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.
## • `` -> `...1`
plot(sales ~ radio, data = ad_sales)
fit <- lm(sales ~ radio, data = ad_sales)
summary(fit)
##
## Call:
## lm(formula = sales ~ radio, data = ad_sales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.7305 -2.1324 0.7707 2.7775 8.1810
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.31164 0.56290 16.542 <2e-16 ***
## radio 0.20250 0.02041 9.921 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.275 on 198 degrees of freedom
## Multiple R-squared: 0.332, Adjusted R-squared: 0.3287
## F-statistic: 98.42 on 1 and 198 DF, p-value: < 2.2e-16
library(readr)
library(readr)
library(ggplot2)
ggplot(ad_sales, aes(x=radio)) +
geom_histogram(binwidth=10, fill="grey20")
Bivariate Analysis Definition & Example https://www.statisticshowto.com/bivariate-analysis/#:~:text=Bivariate%20analysis%20means%20the%20analysis,the%20variables%20X%20and%20Y.
https://www.sciencedirect.com/topics/mathematics/bivariate-data