For Apple's (NASDAQ:AAPL) fiscal 2015 first quarter, analysts have big expectations -- the biggest ever, in fact. Riding on what analysts believe to be record iPhone sales, analysts predict that Apple will report both record revenue and EPS when the company reports its Q1 results on Tuesday, Jan. 27.

iPhone 6. Image source: Apple.

The numbers
The current consensus estimate for Apple's revenue and EPS for Q1 is $67.3 billion and $2.59, respectively. These figures are up 17% and 25% from year-ago record metrics. These big expectations highlight just how bullish the consensus is for Apple in Q1.

The star of the show will undoubtedly be Apple's iPhone. Based on Fortune's panel of Apple analysts, which includes 18 professional and 12 independent analysts, the consensus for iPhone sales in Q1 is 66.5 million, up 30% from the year-ago quarter.

Even more, Fortune's Philip Elmer-DeWitt notes that analyst estimates for holiday iPhone sales has been on the rise as the Apple earnings date approaches.

"On Tuesday, for example, Morgan Stanley's Katy Huberty told clients she now expects iPhone shipments of 67-69 million, well above her model of 62 million -- which remains unchanged, higher only than Gene Munster's 61 million," Elmer-DeWitt said.

The highest estimate in the group comes from independent analyst Kirk Burgess, with an estimate for 71.5 million. But the well-connected KGI Securities' analyst Ming-Chi Kuo, who is not included in Fortune's panel, is also predicting 71.5 million iPhone sales.

What's so important about iPhones in Q1?
Just how key are iPhones to Apple's results? Consider this: Not only is the iPhone segment Apple's most profitable, but it also accounts for the largest portion of the company's revenue -- especially during Q1 since it's the first full quarter of availability of Apple's new iPhone models. Further, if Apple really does sell 66.5 million iPhones in Q1, iPhone sales could account 63% or more of Apple's revenue during the quarter, up from 56% of Apple's revenue in Q4. Comparably, Apple's second and third largest segments, Mac and iPad, accounted for 15.7% and 12.6% of revenue, respectively.

One of the main reasons analysts are bullish on Apple's iPhone sales for Q1 is because its foray into smartphones with larger displays with its iPhone 6 and iPhone 6 Plus put Apple squarely into the middle of a market that was already proven to be big. Pent-up demand for an iPhone with a larger display, therefore, could mean a higher than usual upgrade cycle for existing iPhone users as well as many Android switchers.

Image source: Apple.

Apple's iPhone sales during the first quarter of availability of a new model are typically limited by supply, not demand -- and Q1 was no exception. But, as evidenced by decreasing online wait times for iPhone shipments during the quarter, the tech giant made significant progress toward availability throughout the quarter. And in every first full quarter of new iPhone model sales so far, Apple has been able to significantly boost production compared to the year-ago quarter; Q1 is probably no exception.

Apple's first-quarter results are usually available after market close at this link. Shortly after the figures are released, Apple will host a conference call to discuss the results, followed by a question and answer session with analysts, at 5 p.m. ET on the same day.

Check back with The Motley Fool for Foolish analysis of the results.