Preheat oven to 350℉ and spray a 9-inch loaf pan with cooking spray.
Add flour, baking powder, baking soda, and salt to a bowl and mix with a wire whisk or fork until evenly blended.
In a separate, larger bowl, add oil, sugar, eggs, yogurt, and vanilla. Mix using a whisk, spatula, or spoon until evenly blended.
Add dry ingredients to the wet ingredients bowl. Mix until lumps have mostly disappeared, being careful not to over-mix (so do this manually rather than with a mixer).
Transfer batter to the prepared loaf pan. Sprinkle raspberries on top and gently press them partway into the batter.
Sprinkle crumb topping on top, gently squeezing fingers while doing so to create larger crumbs.
Bake for 55-65 minutes. When done, test with a toothpick—when inserted into the cake, it should come out clean and free of batter. If the raspberries are in the way and making it difficult, gently move some aside with a butterknife and try again.
When baked, allow to cool. Transfer to a wire rack when safe to do so.