To find the least-squares regression model, use the lm() command. From that result, we can find the standard error.

We will use the cholesterol data from Section 14.1, Table 1.

Age <- c(25, 25, 28, 32, 32, 32, 38, 42, 48, 51, 51, 58, 62, 65)
Total_Cholesterol <- c(180, 195, 186, 180, 210, 197, 239, 183, 204, 221, 243, 208, 228, 269)

Now, find the least-squares regression model and use the summary() command.

lm_object <- lm(Total_Cholesterol ~ Age)
summary(lm_object)
## 
## Call:
## lm(formula = Total_Cholesterol ~ Age)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -27.114 -13.405  -3.117  12.575  34.482 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 151.3537    17.2838   8.757 1.47e-06 ***
## Age           1.3991     0.3917   3.571  0.00384 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.48 on 12 degrees of freedom
## Multiple R-squared:  0.5153, Adjusted R-squared:  0.4749 
## F-statistic: 12.76 on 1 and 12 DF,  p-value: 0.003842
# NOTE: If you only want the standard error, enter the code
#
# summary(lm_object)$sigma

The standard error is found under “Residual standard error”. So, the standard error is 19.48.