2025-10-23
Linear regression is a statistical method for modeling the relationship between:
It can be applied to various fields across math, engineering, and computer science! For example, we can use it to predictive machine learning models to predict various values, like housing prices.
Linear Regression models have a linear relationship where:
\[Y = \beta_0 + \beta_1 X + \epsilon\]
Each variable in the Y:
The dataset that will be used is the “women” dataset to model our simple linear regression. We will look at the relationship between height and weight in this dataset.
summary(women)
height weight Min. :58.0 Min. :115.0 1st Qu.:61.5 1st Qu.:124.5 Median :65.0 Median :135.0 Mean :65.0 Mean :136.7 3rd Qu.:68.5 3rd Qu.:148.0 Max. :72.0 Max. :164.0
View(women)
Using this dataset, the goal is to predict the weight of the women based on the height using a simple linear regression model defined earlier, where:
\[Y = \beta_0 + \beta_1 X + \epsilon\]
Each variable in the Y:
In this dataset, we can see that this is a linear relationship between weight and height, which could be used to fit a linear regression model!
The linear regression is the line of best fit of the data.
The predicted weight at a height of 64 inches is 132 pounds.
<ggplot2::labels> List of 3 $ x : chr "Height (inches)" $ y : chr "Weight (pounds)" $ title: chr "Weight vs Height"
We can also get a quick overview and summarization of the data outside of the plots as well, using the following R code below.
Call:
lm(formula = weight ~ height, data = women)
Residuals:
Min 1Q Median 3Q Max
-1.7333 -1.1333 -0.3833 0.7417 3.1167
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -87.51667 5.93694 -14.74 1.71e-09 ***
height 3.45000 0.09114 37.85 1.09e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.525 on 13 degrees of freedom
Multiple R-squared: 0.991, Adjusted R-squared: 0.9903
F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14