How to Perform Multiple Linear Regression in R with the Birthweight Dataset

In practical analysis, several independent variables often determine a single dependent variable. The multiple linear regression equation can be written in matrix form, where the response vector, predictor matrix (including a constant term), and coefficient vector are defined, allowing coefficient estimation via matrix operations, though manual calculation is difficult.

In R, the lm() function is used for this analysis.

Example: using the birthwt dataset to study factors influencing newborn weight and predict weight based on these factors.

<code>library(MASS)
data(birthwt)
birthwt.lm <- lm(bwt ~ age + lwt + as.factor(race) + smoke + ptl + ht + ui + ftv, data = birthwt)
summary(birthwt.lm)
</code>

Result:

<code>Call:
lm(formula = bwt ~ age + lwt + as.factor(race) + smoke + ptl + 
    ht + ui + ftv, data = birthwt)

Residuals:
     Min       1Q   Median       3Q      Max 
-1825.26 -435.21   55.91  473.46 1701.20 

Coefficients:
                     Estimate Std. Error t value Pr(&gt;|t|)    
(Intercept)          2927.962   312.904   9.357  &lt; 2e-16 ***
age                  -3.570     9.620  -0.371 0.711012    
lwt                   4.354     1.736   2.509 0.013007 *  
as.factor(race)2   -488.428   149.985  -3.257 0.001349 ** 
as.factor(race)3   -355.077   114.753  -3.094 0.002290 ** 
smoke               -352.045   106.476  -3.306 0.001142 ** 
ptl                 -48.402   101.972  -0.475 0.635607    
ht                  -592.827   202.321  -2.930 0.003830 ** 
ui                  -516.081   138.885  -3.716 0.000271 ***
ftv                  -14.058    46.468  -0.303 0.762598    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 650.3 on 179 degrees of freedom
Multiple R-squared:  0.2427, Adjusted R-squared:  0.2047 
F-statistic: 6.376 on 9 and 179 DF,  p-value: 7.891e-08
</code>

Plotting the results:

<code>par(mfrow = c(2,2))
plot(birthwt.lm)
</code>

The regression model relates newborn weight (bwt) to maternal age (age), race, smoking status (smoke), hypertension history (ht), uterine irritability (ui), and pre‑pregnancy weight (lwt). Not all variables need to be included; variable selection is challenging and part of model evaluation. In this example, race, smoke, ht, ui, and lwt show statistically significant effects, consistent with an ANOVA on the model. Model assessment can use R‑squared, Adjusted R‑squared, and optionally AIC or BIC (not shown by summary() ). Diagnostic plots of residuals help judge model adequacy and identify outliers or high‑leverage points, which may be removed for a better fit.

Categorical variables are converted to dummy variables using factor() ; for example, the variable race is encoded into two dummy variables representing three categories. The relevel() function can be used to set the reference level.