# Partial residual plot with confidence intervals in R for multivariate generalized linear regression

I have fit the following regression model:

```
mod <- betareg(connectance ~ fc * size, data = net.land.3000, link = "logit")
summary(mod)
Call:
betareg(formula = connectance ~ fc * size, data = net.land.3000, link = "logit")
Standardized weighted residuals 2:
Min 1Q Median 3Q Max
-2.4777 -0.1919 -0.0185 0.1435 2.6781
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.160853 0.939846 -2.299 0.0215 *
fc 0.062797 0.027081 2.319 0.0204 *
size 0.109050 0.101085 1.079 0.2807
fc:size -0.005822 0.003427 -1.699 0.0894 .
Phi coefficients (precision model with identity link):
Estimate Std. Error z value Pr(>|z|)
(phi) 85.06 42.32 2.01 0.0445 *
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Type of estimator: ML (maximum likelihood)
Log-likelihood: 12.88 on 5 Df
Pseudo R-squared: 0.6826
Number of iterations: 35 (BFGS) + 3 (Fisher scoring)
```

I am trying to plot the relationship between `fc`

and `connectance`

, with the effects of `size`

and the `fc * size`

interaction taken into account, and with a 95% confidence interval. From what I understand, this is a partial residual (or marginal effects) plot.

How can I create one in R given that I have multiple independent variables, an interaction, and a non-linear regression? I know the standard method would be to regress the residuals of (y ~ my other independent variables) vs. (my variable of interest ~ other independent variables), but I'm not sure how to handle that with the interaction and non-linear relationship.

I have given it a shot using the `plot_model()`

function and got the following:

```
plot_model(mod, type = "pred", terms = "fc")
```

However, I was expecting the regression line in my partial residual plot to have a slope equal to the model estimate for `fc`

(0.06) and an intercept equal to the intercept in my model output (-2.16), which it does not.

To summarize my questions:

- Is what I want a partial residual plot?
- If yes, how is that related to the slope of my variable of interest in my model output, if at all?
- Is
`plot_model`

giving me the correct results, or is there another function I can use to calculate a regression line and confidence interval?

Sorry if this is very confusing, I am something of a beginner at stats and quite confused. I would appreciate any help, and be happy to provide more information as it is useful!

For reference, here are my data:

```
connectance fc size
1 0.3333333 37.96319 8
3 0.2500000 11.33780 8
5 0.3809524 18.16915 13
6 0.5000000 47.88571 5
8 0.2500000 14.02959 10
9 0.1904762 17.87691 13
11 0.2777778 19.11214 9
12 0.2291667 29.03701 14
```