# Does it make sense to use the slope of trend line from a regression as a ratio between x and y

The regression plots Hours (y) vs jobs (x). Let's say the equation is: y = 0.4x + 90

Is it okay to say that the time for each job is 0.4 hours?

• The incremental time for each job is 0.4 hours. For the actual time you have to take into account the 90 hour constant – Jake Westfall Jan 22 at 21:12
• The estimate of the expected marginal time for each job would be 0.4 hours (i.e. adding a job will on average add 0.4 hours). It may be that no job will take 0.4 hours, even on average, because that intercept term is large - it depends on how that 90 is allocated to jobs – Glen_b Jan 22 at 23:15

I presume $$x$$ is number of jobs and $$y$$ is number of hours to complete it. It's not correct to say that time for each job is 0.4 hours because you have a (pretty large) bias term. This means you have a fix cost. Performing one job takes $$90.4$$ hours, two jobs $$90.8$$ hours etc. So, you can say that each additional job takes 0.4 hours. And, time for each job asymptotically approaches $$0.4$$ hours, i.e. as $$x\rightarrow \infty$$.
Not exactly. Assuming a simple linear model $$y = \beta_0 + \beta_1 x + \epsilon$$, the parameter $$\beta_1$$ (in this case $$0.4$$) represents the effect of a one-unit change in the corresponding $$x$$ (here jobs) covariate on the mean value of the dependent variable, $$y$$ (here hours), assuming that any other covariates remain constant at some value. As the $$\beta_0$$ (the intercept) is $$90$$, probably there are some other factors that require on average $$90$$ hours to be taken into account. It is more relevant to say that each additional job requires an additional $$0.4$$ hours.