Helen Jackson

Analytic and Research Support

Regression analysis: Weather and agricultural yields

Overview: The thick grey line shows UK yields of the selected crop over the period 1985-2012. The thin grey line (at the end) shows the yields estimated by a regression model1 based on weather variables such as temperature and rainfall. The coloured lines show how yields would have improved given optimal2 conditions for the weather variable shown, all else being equal, according to the regression model. This gives a visual impression of how influential each weather variable is.

Interpretation: At the national scale, weather appears, perhaps unsurprisingly, to account for a large amount of the variation in crop yields. Measures of how well the model fits the data (see below) are reasonable. Some degree of error in the estimate due to unknown factors (e.g. prevalence of particular practices or crop varieties in that year) is inevitable. If more detailed data at a localised level – for example, nutrient loads and land management practices – could be taken into account by the model, we might expect a better fit.

For wheat, the most important climatic influences appear to be a warm summer to ripen the wheat and a frosty December (presumably to kill off pests and diseases). Surprisingly, and contrary to what is commonly claimed, rainfall in summer or August did not appear to be highly significant. Oats appear to need a good spring in order to get established when they are sown (particularly a dry March with not too much frost), and summer warmth. In addition, a 'double whammy' of cold springs and excessive summer rainfall seem to have suppressed yields in some years. (Maincrop) potatoes seemed strongly affected only by summer weather: temperature in late summer, drought and summer frost.

Results: The regression coefficients for wheat are as follows (click on the appropriate button at the top for the other crops' results):

CoefficientEstimateSignificant at α
Mean summer temperature0.55  0.001
Days airfrost in Dec0.0670.001
Rainfall in previous Nov-0.0050.05  
Dummy: total rainfall in Feb and March > 205mm-0.68  0.001
R2 = 0.709       Adjusted R2 = 0.658

About the data: Monthly weather data is from the UK Meteorological Office. UK averages are used for the wheat and potato charts, but Scottish averages are used for the oats chart, given that the bulk of UK oat production is in Scotland.

Agricultural yield data is from the UK Department for Environment, Food and Rural Affairs' Agriculture in the UK data series. Yields of only maincrop (as opposed to early) potatoes were considered. Some crops have two different sowing seasons, or long harvest periods. The analysis is limited by the fact that yield data is not disaggregated by sowing season or harvest period. For example, weather in August could not be expected to affect potatoes harvested in July, but it could affect potatoes harvested in September; spring and winter wheat might be affected differently by weather during a particular month. This could account for some of the unexplained variation.


1 Regression analysis examines whether and by how much variation in one or more variables is associated with variation in another. The model used here is ordinary least squares.

2 The optimum is defined as the maximum or minimum of the weather variable over the period (depending on whether the weather variable has a beneficial or adverse effect).