Upon observing the results with the 5-point smoothing, a trend appears. Take the data from the 5-point moving average smoothing and fit a straight line using the least-squares method. Put the first smoothed point at t = 3 and then centre the time data. State the y-intercept and gradient. Compare this trend line with that from question 3.
i'm confused on how to centre the time data or what is meant by that, can someone please explain this to me?
You'd only centre the data during (even number)-pt moving mean smoothing such as 2-pt, 4pt etc.
This is because when you initially find the mean, the centre of the points is not actually belonging to the original series (or original time value). We then have to 'centre' the means through finding the 2-pt moving mean again of the already smoothed values in order to allow them to line up with their original time values.
This is would be better demonstrated using a visualised table, so perhaps try drawing one out!
However, in your case of a 5-pt moving mean or any (odd number)-pt moving mean, centring would definitely not be required. Perhaps it was a trick or a typo in the question that was provided to you so don't stress!
Hope I helped