Phenomenological relations exist between the peak luminosity and other observables of type Ia supernovae (SNe Ia) that allow one to standardize their peak luminosities. However, several issues are yet to be clarified: SNe Ia show colour variations after the standardization. Also, individual SNe Ia can show residuals in their standardized peak absolute magnitude at the level of similar to 0.15 mag. In this paper, we explore how the colour and luminosity residual are related to the wavelength shift of nebular emission lines observed at greater than or similar to 150 d after the maximum light. A sample of 11 SNe Ia which likely suffer from little host extinction indicates a correlation (3.3 Sigma) between the peak B - V colour and the late-time emission-line shift. Furthermore, a nearly identical relation applies for a larger sample in which only three SNe with B - V greater than or similar to 0.2 mag are excluded. Following the interpretation that the late-time emission-line shift is a tracer of the viewing direction from which an off-centre explosion is observed, we suggest that the viewing direction is a dominant factor controlling the SN colour and that a large part of the colour variations is intrinsic, rather than due to the host extinction. We also investigate a relation between the peak luminosity residuals and the wavelength shift in nebular emission lines in a sample of 20 SNe. We thereby found a hint of a correlation (at similar to 1.6 Sigma level). The confirmation of this will require a future sample of SNe with more accurate distance estimates. Radiation transfer simulations for a toy explosion model where different viewing angles cause the late-time emission-line shift are presented, predicting a strong correlation between the colour and shift, and a weaker one for the luminosity residual.