The relationship between annual average temperature over 10 years in various towns and the area of the UK in which the town is located was investigated. Area is described as being one of five ordered categories A, B, C, D, E from north to south, with A being the most northerly (i.e Scotland) and E being the most southerly.
(i) One investigator codes A, B, C, D, E as 1,2,3,4,5 respectively, and the fits the regression $E(Y_{i}) = \mu_{i} = \beta_{0} + \beta_{1}x_{i}$ where $Y_{i}$ is the annual average temperature and $x_{i}$ the coded as area. Explain the interpretation of $\beta_{1}$
My thoughts:
I know $\beta_{1}$ is the gradient of the graph but I am struggling to define it in context. Is it the average change in temperature per year? I can't tell what $x_{i}$ is from the question, is it a unit of time or Area?