Improve the bracketed part of the sentence by choosing the best alternative: We (are looking forward for) a positive response from you.

Introduction / Context:
This question tests a very common collocation in English: "look forward to" followed by a noun or an -ing form. Sentence improvement items like this check whether the learner knows which preposition correctly completes the phrase. Many speakers mistakenly say "look forward for" or "look forward at", so examinations frequently include this error to distinguish accurate usage from incorrect patterns.

Given Data / Assumptions:

• The original sentence is: "We (are looking forward for) a positive response from you."
• The bracketed portion is grammatically suspect and needs to be improved.
• Four alternatives are provided, including "No improvement".
• We assume the intended meaning is that the speaker eagerly awaits a positive reply.

Concept / Approach:
In English, the fixed phrase is "to look forward to something" or "to look forward to doing something". The preposition "to" is an integral part of the expression. It does not change according to the object. "For" and "at" are incorrect in this collocation. The tense "are looking forward to" is also appropriate here because it describes a present, ongoing expectation.

Step-by-Step Solution:
Step 1: Isolate the phrase "are looking forward for" and recall the correct form from standard English usage.Step 2: Recognise that the correct collocation is "are looking forward to".Step 3: Examine option A: "are looking forward to". This matches exactly the correct collocation and tense.Step 4: Examine option B: "have been looking forward at". Both the preposition "at" and the tense change are unnecessary and unidiomatic here.Step 5: Examine option C: "should look forward at". Again, "at" is wrong, and "should look" changes the meaning from a simple statement to advice.Step 6: Option D, "No improvement", would keep the incorrect "for", so it cannot be correct.Step 7: Conclude that option A is the only grammatically correct and idiomatic improvement.

Verification / Alternative check:
Rewrite the full sentence with option A: "We are looking forward to a positive response from you." This sounds natural and is frequently used in formal letters and emails. We can compare with typical closing lines such as "We look forward to hearing from you soon." If we replace "to" with "for" or "at", both native and fluent speakers will immediately perceive it as incorrect: "looking forward for a response" is not standard English. Hence, the selected option is verified as correct.

Why Other Options Are Wrong:
"Have been looking forward at" (option B) mixes the present perfect continuous tense with an incorrect preposition and is far more complicated than needed. "Should look forward at" (option C) uses "at" wrongly and gives a sense of advice, not description. "No improvement" (option D) would leave the clearly incorrect "for" unchanged. None of these reflect the fixed phrase "look forward to" that is widely accepted in English.

Common Pitfalls:
Many learners try to choose prepositions based on general meaning instead of memorising fixed expressions. They think "for" fits because we wait "for" something. However, phrasal verbs and idiomatic expressions often fix a particular preposition that does not follow simple logic. A useful strategy is to learn expressions like "look forward to", "interested in", and "good at" as complete chunks rather than word by word.

Final Answer:
The correct improvement is "are looking forward to".