# On a finite time scale

**MeanMean**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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It was rumored that updates to the MacBook Pro were coming at WWDC. These rumors did not pan out. Instead it looks like the new MacBook Pro will be landing sometime later this year, possibly due to delays in availability of high end Skylake 45w mobile parts. This seems plausible, given that Intel only released its Skylake quad core NUC in mid-May. The magnitude of these delays has certainly made its way around the tech press, but are these delays really exceptional?

This quick exploratory analysis of the significance of these delays was performed using historical delays between iterations. The source of this release dates was from the Wikipedia pages for each of these products. A csv file including this data has been made available here. For the retina and non-retina release dates are given for only the retina versions of products once they become available.

Notably absent from this analysis is the MacBook Air and MacBook. In the former case the dates were not present on the Wikipedia article, and in the later case there wasn’t sufficient data to do anything but interpolate.

## Overview

For this exploratory analysis two models were used. The first model, linear regression with one predictor (see Figure 1.), assumes that there is a constant interval between releases over time. Deviations from this release cycle are just model error. The second model is a differenced regression model. In this linear model, release dates are replaced with differences between release dates. This allows for a trend in the release dates, such as increasing delays between releases.

This analysis treats future releases and delays as a prediction problem. Therefore, prediction intervals are used to determine significance. The level of significance is set to 5% for the two sided interval, however our interest is really at large delays giving us a one-sided confidence level of to 2.5% for our analysis. Inference including point estimates and prediction intervals are based on standard ordinary least squares (OLS) assumptions. In both models, time is treated as the dependent variable with product iteration as the independent variable. Time is represented as days since epoch, where epoch is set at 0 equal to January 1, 1970.

This problem is actually a wait-time problem, so normality is used as an approximation to modeling with gamma distributed errors or other slightly more difficult approaches. Still, the regression approach seems to be ‘good enough’ for this blog post. In the future I’ll revisit more complex models.

macRelease <- read.csv('macrelease.csv') macRelease$releaseDate <- as.Date( macRelease$Release.date, format="%d %B %Y") library(ggplot2) theme_set(theme_gray(base_size = 20)) # plot product release dates by iteration p <- ggplot(macRelease, aes(x=Iteration, y=releaseDate, group=Product)) p + geom_line(aes(color=Product),size=1) + geom_point(aes(color=Product),size=3) + labs( title='Apple Product Iteration by Release Date', y="Release Date")