Change Dash Type on Trend Line

I don't think you can do that using the built in trendlines. The way I would do this is to build the regression in the spreadsheet, then use the regression data from the spreadsheet to add my own trendline as a second and third data series. I would expect something like:

1) A column of 1,2,3,4,5,6,7 for the regression functions.
2) SLOPE() and INTERCEPT() functions to compute the regression (I'm assuming you want a simple linear regression. If you want a more complex regression, then adjustments will need to be made).
3) A column to compute the trendline for the entered points.
4) A column to compute the trendline for the blank points.
5) Add columns 3 and 4 to the chart as two new data series.
6) Format the new data series as desired.

With that overview, where do you get stuck?

It looks like you can do this by using 2 series and 2 trend lines.

The second data series is adjusted to only include those cells with data.
Add trend line to both series.

The trend line on the complete data set is used to display the dashed trend line segments.
The trend line on the incomplete data set is used to display the solid trend line segments.