Negative prediction values from linear regression in R So I made a linear regression in R Studio to predict the price of a car based on the year of fabrication. The data set is called "audi" and my linear regression looks like this:
library(tidyverse)
library(modelr)
...
model_price_Year <- lm(data = audi, price ~ year)
summary(model_price_Year)

The result of the summary is this:
Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -6.437e+06  8.503e+04  -75.71   <2e-16 
year         3.203e+03  4.215e+01   75.98   <2e-16 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9437 on 10666 degrees of freedom
Multiple R-squared:  0.3512,    Adjusted R-squared:  0.3511 
F-statistic:  5772 on 1 and 10666 DF,  p-value: < 2.2e-16

Then, I made a grid and i added predictions for 100 values of the year. It looks like this:
grid_year <- audi %>%
  data_grid(year = seq_range(year, 100)) %>%
  add_predictions(model_price_Year, "price")

And after that, if i want to see results, they look like this:
  year   price
   <dbl>   <dbl>
 1 1997  -41481.
 2 1997. -40737.
 3 1997. -39993.
 4 1998. -39249.
 5 1998. -38505.
 6 1998. -37761.
 7 1998. -37017.
 8 1999. -36273.
 9 1999. -35529.
10 1999. -34785.

They are all negative, and becuase we are talking about the price, it doesnt really make sense. Why are they negative? How do I interpret this?

You didn't constrain the output. Without such a constraint, you allow for any real number to be predicted, including numbers that are ridiculous. For instance, logistic regressions constrain the probability predictions to $[0,1]$ by applying a link function that compresses the real line to the unit interval.
An alternative might be to fit a log-linked gamma generalized linear model or a log-linked Gaussian generalized linear model.
A negative price might make sense, but the interpretation would be that, instead of selling the car, you pay someone to take it off your hands. I could imagine this for someone who has a useless item that is expensive to store, so you hire someone to take it away.
It also might be that the year is not a linear predictor of price. I would guess that prices don't just increase by a fixed amount every year. If the price of a car goes up $X\%$ each year (nonlinear), that's different than the price going up $\$Y$ every year (linear).
