Base R

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)
Cholesterol <- c(180, 195, 186, 180, 210, 197, 239, 183, 204, 221, 243, 208, 228, 269)
Table1 <- data.frame('Age'=Age, "Cholesterol"=Cholesterol)
head(Table1)
##   Age Cholesterol
## 1  25         180
## 2  25         195
## 3  28         186
## 4  32         180
## 5  32         210
## 6  32         197

Find the least-squares regression model and save it as an object. Use the summary() command on the object to obtain the regression output.

lm_object <- lm(Cholesterol ~ Age, data=Table1)
summary(lm_object)
## 
## Call:
## lm(formula = Cholesterol ~ Age, data = Table1)
## 
## 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

The test statistic for the explanatory variable, Age, is 3.571 and the P-value is 0.00384 (under Coefficients: in the output).

Mosaic

Mosaic allows the user to only show the output desired. Consider the msummary() command on the lm_object.

library(mosaic)
lm_object <- lm(Cholesterol ~ Age, data=Table1)
msummary(lm_object)
##             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 ** 
## 
## 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

The test statistic for the explanatory variable, Age, is 3.571 and the P-value is 0.00384.

The coef(summary()) command on the lm_object provides just the inference on the slope and intercept of the linear model.

library(mosaic)
lm_object <- lm(Cholesterol ~ Age, data=Table1)
coef(summary(lm_object))
##               Estimate Std. Error  t value     Pr(>|t|)
## (Intercept) 151.353658 17.2837604 8.756987 1.472754e-06
## Age           1.399064  0.3917375 3.571433 3.842261e-03