Obtaining a model

Inserting a linear trend line, sometimes called a line of best fit.

• The gradient of the line matches the overall trend of the data

• The line passes through as many points as possible

• There are as many points on one side of the line as the other

Interpreting the gradient

A linear trend line suggests that the response variable, Y, changes by a fixed amount for each unit change in X. So if the trend line has equation y = 5x + 7 the gradient is 5, Y changes by 5 units for every change of 1 unit in X. It is important to refer to the units when describing the gradient or rate of change of Y as X changes.

Describing its appropriateness

• What does the correlation coefficient say about the model?

• For what range of values (x-variable) can this model be applied?

• Is the linear model appropriate everywhere in this range?

• What is the range of values that predictions are likely to lie in?
  (Limits of the band)

• What does the gradient of the regression line tell us about the relationship between the variables?
  Does this relationship seem reasonable?