What exactly does "Speed" affect?

Character customization allows for modifications to a character's attack, defense, and speed. Attack improves outgoing damage and knockback. Defense reduces incoming damage and knockback, improves shield strength, and increases the "perfect shield" timing window. So what exactly does speed affect? Please provide evidence.

Possible factors to consider:

• Dash speed
• Walking speed
• Air speed
• Fall speed
• Jump height
• Attack execution time
• Time between attacks
• Recovery time
• Directional influence
• Dash attack travel distance
• Dodge roll travel distance
• Smash attack charge time
• Dashing turn time

Solution 1:

Raising speed will:

• Raise Dash speed
• Raise Walking speed
• Raise Air speed
• Raise Jump Height
• Raise dash turn time
• Lower Attack damage
• Lower Launch distance
• All others unaffected.

Raising defense will lower everything that speed will raise. Raising attack will not affect speed, but will lower defense. (It's hard to provide evidence, but you can just see for yourself.)

Solution 2:

Equipment comes in various types, which each have three rarities. Higher rarities result in stronger stat modifications. If a piece of equipment has an extra effect, it does not show its rarity. The frequency rate of each type of equipment appears to be based on how many characters can utilize it - for example, Swords are much more common than Pikmin.

Speed equipment increases walking, dashing, air speed, jump height, and fast-falling speed. Reduces landing lag, but does not increase gravity, nor falling speed. Positive speed values will lower the fighter's weight limit for holding Smash Run powers, while negative speed values increase the weight limit.

There are a lot of equipment pieces, so if you want to take a look at them all, I've included a link to the wiki.