Open your image.
Make two duplicates. Turn off the original layer.
Select/Highlight the uppermost layer.
Convert the uppermost layer into a Smart Object. (Right click the layer and select "Convert to smart object".
Select your Rectangular Marquis Tool and set the feather to 25px.
Make a selection of the area you wish to blur.
Go to FILTER > BLUR > GAUSSIAN BLUR, and adjust (I used 8.0). Since this was added to a smart object it's called a smart filter and can be edited.
Layers Panel.
Another very easy way to do this would be to just blur the entire uppermost layer (that is a smart object) and use a layer mask with a gradient.