Bu çıkarımın dayanağı yalnızca bir varsayım.

A natural breakdown is:

• Bu = this
• çıkarım-ın = of the inference / of the conclusion
  
  • çıkarım = inference, conclusion
  • -ın = genitive ending, meaning of
• dayanağ-ı = its basis / its support
  
  • base form: dayanak = basis, support, foundation
  • -ı = 3rd person possessive ending, giving its basis
• yalnızca = only, merely, just
• bir = a/an
• varsayım = assumption

So the structure is basically:

Bu çıkarımın dayanağı + yalnızca bir varsayım
= The basis of this inference is only an assumption.

Because Turkish often uses a genitive + possessed noun structure where English would use of or 's.

Here:

• çıkarım = inference
• çıkarımın = of the inference / the inference's

The ending -ın is the genitive suffix. Its form changes by vowel harmony:

• -ın
• -in
• -un
• -ün

Since çıkarım has the vowel ı, the correct form is -ın.

So:

• bu çıkarımın = of this inference / this inference's

This happens for two reasons:

1. The noun is in a possessed form
   In Turkish, when you say something like the basis of X, the possessed noun takes a possessive ending.

   • dayanak = basis
   • dayanağı = its basis

2. The final k softens to ğ before a vowel
   This is a common sound change in Turkish.

So:

• dayanak
  • -ı → dayanağı

Together with çıkarımın, you get:

• çıkarımın dayanağı = the basis of the inference

This pattern is very common in Turkish:

• evin kapısı = the door of the house
• kitabın adı = the name of the book
• çıkarımın dayanağı = the basis of the inference

Yes, literally it is very close to this inference's basis.

But in natural English, you would usually say:

• the basis of this inference
• the support for this inference

Turkish commonly expresses this relationship with the possessor first:

• bu çıkarımın = of this inference
• dayanağı = its basis

So even though the literal shape is like this inference's basis, the natural translation is usually the basis of this inference.

Because Turkish often leaves out the verb to be in the present tense, especially in the 3rd person.

So:

• Bu çıkarımın dayanağı yalnızca bir varsayım. = The basis of this inference is only an assumption.

There is no separate word like English is here, but the sentence is still complete.

You could also say:

• Bu çıkarımın dayanağı yalnızca bir varsayımdır.

The ending -dır adds a more formal, assertive, or explanatory tone. In everyday Turkish, leaving it out is very normal.

Yalnızca means only, merely, or just.

In this sentence, it limits bir varsayım:

• yalnızca bir varsayım = only an assumption
• more naturally: merely an assumption / just an assumption

So the sentence is emphasizing that the basis is not strong evidence, but only a hypothesis/assumption.

A close synonym is sadece:

• yalnızca bir varsayım
• sadece bir varsayım

Both are common. Yalnızca can sound a little more formal or written.

Bir here works like a/an in English.

So:

• bir varsayım = an assumption

In predicate sentences like this, both forms can exist, but bir varsayım sounds very natural because it presents the thing as one example of a category:

• O bir doktor. = He is a doctor.
• Bu yalnızca bir varsayım. = This is only an assumption.

Without bir, the sentence can still be possible in some contexts, but it may sound more general, compressed, or label-like. Here, yalnızca bir varsayım is the most natural phrasing.

In this sentence:

• Bu çıkarımın dayanağı = the thing being talked about
• yalnızca bir varsayım = what is being said about it

So structurally:

• Subject/topic: Bu çıkarımın dayanağı
• Predicate: yalnızca bir varsayım

That is why the sentence feels like an equation:

The basis of this inference = only an assumption

This is a very common Turkish sentence pattern.

Because bu is modifying çıkarım:

• bu çıkarım = this inference
• bu çıkarımın = of this inference

So the meaning is:

• the basis of this inference

If bu were placed differently, the meaning emphasis could change. For example:

• bu dayanak = this basis
• çıkarımın bu dayanağı = this basis of the inference

But the given sentence is specifically about this inference, not about choosing among several possible bases.

No, this is very normal Turkish word order for this kind of sentence.

Turkish often places the predicate at the end, so:

• Bu çıkarımın dayanağı → topic/subject first
• yalnızca bir varsayım → predicate at the end

Also, yalnızca usually comes right before the part it affects:

• yalnızca bir varsayım = only an assumption

So the sentence is arranged in a very standard, clear way.

These are the main points:

• ç = like ch in church
• ı = a Turkish vowel with no exact English equivalent
  It is a back, unrounded vowel. It is not the same as English i.
• ğ = usually not pronounced like a hard g
  It often lengthens the previous vowel or creates a very soft glide.

So in this sentence:

• çıkarımın has both ç and ı
• dayanağı has ğ

A learner-friendly way to think of them:

• çıkarımın: the first sound is ch, and the ı sounds should not be pronounced like English ee
• dayanağı: do not pronounce the ğ as a strong g; keep it soft

If you want, a good next step is to listen to native audio and repeat slowly, because ı and ğ are much easier to learn by ear than from English spelling.

Yes. In most contexts, that would work perfectly:

• Bu çıkarımın dayanağı yalnızca bir varsayım.
• Bu çıkarımın dayanağı sadece bir varsayım.

Both mean essentially the same thing: The basis of this inference is only an assumption.

A rough nuance:

• sadece = very common in everyday speech
• yalnızca = also common, sometimes a bit more formal or written

So for a learner, it is useful to know both.