How to interpret regression equation?

Question

I am trying to understand how to interpret the regression line given:

$y = -5.18 + 1.94x$ (regression line)

where $y$ is number of cold drinks sold and where $x$ is temperature

Interpret values of $a$ and $b$ in context

Interpreting $a$ in context

• To interpret $a$, I substituted $x$ (temp) as $0$.
• This tells me that $y$ (cold drinks sold) is $-5.18$. Therefore, we can interpret that when the temperature is $0$ degrees, the number of cold drinks sold is $-5.18$ (But this is impossible?)

How would I interpret $b$ in context as well?

Answer 1

The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).

Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).