How to Illustrate Relationship between Adjusted Variable and Variable of Interest I'll give an example. 
In a simple correlation, blood pressure is associated with body fat. 
However, I want to adjust %body fat for age and sex. So, in SAS, PROC CORR I use age and sex as partial variables and the association remains significant between blood pressure and body fat(adjusted). 
How can I illustrate this in a graph (i.e. blood pressure vs %bodyfat (adjusted))?
My first though was to use a linear regression (PROC REG/PROC GLM) with %bodyfat as the dependent variable and age, sex as the independent/quantitative variables and then output the residuals. Add the mean of %bodyfat to the residuals and then plot this as my y values.
Is this appropriate or is there another way of doing this?
 A: Since you only have two variables you're adjusting for, one of which is a 2-category factor, the easiest way to visualize the whole thing would just be by using some colouring and symbols:
# simulate data
set.seed(1234)
age <- round(rnorm(30, 40, 10))
sex <- round(runif(30, 0, 1))
bodyfat <- rnorm(30, 10 + 5 * sex + age / 10, 3)
bloodpressure <- rnorm(30, 55 + bodyfat * 2 + age / 10, 5)

# plot original with color and pch set to other variables
cols <- colorRampPalette(c("blue", "black", "red"))(30)
par(mfrow = c(1, 1))
plot(bloodpressure ~ bodyfat, col = cols[order(age)], pch = sex + 17)
legend("bottomright", legend = c("male", "female"), pch = 17:18)


You could add a colour scale to your legend for age.

Alternatively, you could adjust bodyfat for age and sex, although this loses its easy interpretation. If you want to adjust as you propose in your question—by regressing body fat on age and sex—you should add the intercept of this model to the residuals, not the mean. 
This is equivalent to subtracting $\beta_1 \cdot \text{age}$ and $\beta_2 \cdot \text{sex}$ from the body fat percentage in:
$$\text{body fat percentage} = \beta_0 + \beta_1 \cdot \text{age} + \beta_2 \cdot{sex} + \epsilon$$
That would look like this:
# plot blood pressure vs adjusted bodyfat
LM <- lm(bodyfat ~ age + sex)
adjusted_BF <- (coef(LM)[1] + resid(LM))
par(mfrow = c(1, 2))
plot(bloodpressure ~ bodyfat)
plot(bloodpressure ~ adjusted_BF)


As expected, the relationship observed in the right scatter plot is slightly weaker after adjusting for the effects of age and sex.

However, looking at partial correlations is more like adjusting both variables for the remaining variables:
LM2 <- lm(bloodpressure ~ age + sex)
adjusted_BP <- coef(LM2)[1] + resid(LM2)
plot(adjusted_BP ~ adjusted_BF)


But again, be careful not to mislead your readers with this, as these axes no longer represent blood pressure and body fat.
A: If you have enough data for each age-group you are interested in, "facets" may be a better way to convey your message than the first graph proposed by @Frans Rodenburg.
Simulate data 
set.seed(1234)
age <- round(rnorm(1000, 40, 10))
sex <- round(runif(1000, 0, 1))
bodyfat <- rnorm(1000, 10 + 5 * sex + age / 10, 3)
bloodpressure <- rnorm(1000, 55 + bodyfat * 2 + age / 10, 5)

Data transformation 
library(tidyverse)

data <- tibble(bodyfat, bloodpressure, age, sex)
data <- data %>%
          mutate(age_group = case_when(age < 25 ~ "0 to 25",
                                       age >= 25 & age < 40 ~ "25 to 40",
                                       age >= 40 & age < 50 ~ "40 to 50",
                                       age >= 50 & age < 60 ~ "50 to 60",
                                       age >= 60 ~ "60 and over"
                                       )) %>%
          mutate(sex = case_when(sex == 0 ~ "female",
                                 sex == 1 ~ "male"))

Data visualization through facets
ggplot(data, aes(bodyfat, bloodpressure)) +
  geom_point() +
  facet_wrap(age_group ~ sex)


