MeanRegressors

XXX

■ Where will iPhone sales go?iPhone 6Sales Projection

October 2014

Who run the world?

Allen MillerPeter SvenssonJing HouleSlava DrukerConnor Wilson

2

MeanRegressors

• Overview & Background

• Full Model

• Best Model

• Predictions

• Conclusions

Agenda

3

MeanRegressors

Predicting Apple product demand:

4

MeanRegressors

Predicting Apple product demand:

5

MeanRegressors

Predicting Apple product demand:

6

MeanRegressors

But seriously...Who should care about Apple’s iPhone sales volumes?

■ Investors

■ Partners

• Wireless Carriers

• Suppliers

■ Competitors

• Hardware manufacturers

• Tech rivals

■ Politicians

■ Journalists

■ Economists

■ Tim Cook and Apple’s other 80k+ employees

7

MeanRegressors

• Overview & Background

• Full Model

• Best Model

• Predictions

• Conclusions

Agenda

8

MeanRegressors

To develop the full model we took into account macro, industry/competitive, and Apple specific factors

1. Text in boxes is centered if no bullet text follows2. Text in boxes is left aligned if bullet text follows below3. Second grey for stand-alone boxes – boxes not in direct combination with light-grey or other color shapes exclusive arrows

Model Factors

Full Model

Macro Industry Apple Specific

• U.S. GDP

• U.S. Retail Sales

• Total Smartphone Sales

• Stock Price

• iPhone Sales

• Existing iPhones

• Market Share

• Launch of iPhones

9

MeanRegressors

Some data was readily available, however, the Apple specific data required mining financial statements and news reports

1. Height of grey column heading with two lines is 0.55” (1.4 cm); Height of grey column head with one line is 0.39” (0,99 cm)2. See table toolbar for column resizing toolsSource: Any data presented in text or chart format should have a source identified; notes and sources are 8 point Arial, regular text

Sources

Input Source Rationale/Methodology

U.S. GDP• Commerce Dept.

• In lieu of global GDP figures we used U.S. GDP which represents the largest market for iPhones as a proxy economic health

U.S. Retail Sales

• Census Bureau

• We used U.S. retail sales as an indicator of strength or weakness in consumer spending and consumption

Total Smartphone Sales

• IDC• Total smartphone sales provides a proxy for the health of the smartphone market

Stock Price• Yahoo Finance

• Quarterly stock price growth indicates the health of Apple

iPhone Sales • 10k/News• Quarterly iPhone sales provide the existing trend and allow us to test our regression

Existing iPhones

• 10k/News • Provides existing penetration of iPhones

Market Share • IDC/Apple • Provides a proxy for iPhone penetration

Launch of iPhones

• 10k/News • Used to understand the impact of new phone releases on sales

10

MeanRegressors

The factors we selected then had to be manipulated to be able to draw conclusions

Manipulations

Original Variables Manipulations for Full Model

Sales

Sales Last Quarter

Log Sales

iPhones Already Sold

Time Dummy Values

2nd Quarter

3rd Quarter

4th Quarter

iPhone Launch

After early new phone

After late new phone

Before early new phone

Before late new phone

Early new phone

Late new phone

US GDP US GDP from Previous Quarter

US Retail Sales % Change in retail sales for quarter based on Quarter t-2 and Quarter t-1

Smartphone Sales iPhone sales based on Quarter t-1

Apple Market Share Apple market share pvs quarter

Stock Price% change in stock price based on average closing stock price in previous

quarters

11

MeanRegressors

The full model regression has a high R2, but this seems to be a case of over fitting somewhere in the modelRegression Statistics

Multiple R 0.99

R Square 0.98

Adjusted R Square 0.96

Standard Error 3.07

Observations 28

df SS MS F Significance F

Regression 16 6524.62 407.79 43.23 0.00

Residual 11 103.76 9.43

Total 27 6628.38

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept -8.81 4.04 -2.18 0.05 -17.71 0.08iPhones already sold -0.14 0.06 -2.44 0.03 -0.27 -0.01Sales last quarter 0.18 0.24 0.77 0.46 -0.34 0.712nd Q -4.59 2.58 -1.78 0.10 -10.27 1.083rd Q -5.85 2.54 -2.31 0.04 -11.44 -0.274th Q -9.90 2.32 -4.27 0.00 -15.01 -4.79After early new phone -1.06 2.97 -0.36 0.73 -7.60 5.48After late new phone 11.95 2.57 4.66 0.00 6.31 17.60Before early new phone 4.54 3.42 1.33 0.21 -2.99 12.08Before late new phone 1.80 2.68 0.67 0.51 -4.10 7.70Early new phone 12.90 3.44 3.76 0.00 5.34 20.46Late new phone 7.21 2.91 2.48 0.03 0.80 13.61US GDP pvs quarter 29.53 34.29 0.86 0.41 -45.94 105.00% Change in US Retail Sales pvs quarter -4.96 51.43 -0.10 0.92 -118.15 108.24IDC smartphone sales pvs quarter 0.38 0.12 3.23 0.01 0.12 0.64Apple market share pvs quarter 18.61 27.79 0.67 0.52 -42.54 79.77% one quarter lagging stock price change based on

average closing stock price in previous quarters2.68 5.87 0.46 0.66 -10.24 15.60

12

MeanRegressors

Additionally, there is multi-colinearity between the various sales data which makes sense given Apples market share

iPhones

already

sold

Sales

last

quarter

2nd Q 3rd Q 4th Q

After

early

new

phone

After

late

new

phone

Before

early

new

phone

Before

late

new

phone

Early

new

phone

Late

new

phone

GDPRetail

Sales

Smartp

hone

Sales

Market

Share

Stock

price

iPhones already sold 1.000

Sales last quarter 0.927 1.000

2nd Q 0.038 0.205 1.000

3rd Q 0.116 0.107-0.333 1.000

4th Q -0.105 -0.196-0.333 -0.333 1.000

After early new phone -0.092 0.063 0.160 -0.160 -0.160 1.000

After late new phone 0.015 -0.106-0.269 -0.269 0.377 -0.129 1.000

Before early new phone -0.147 -0.133-0.160 0.160 0.160 -0.077 -0.129 1.000

Before late new phone 0.234 0.224 0.162 0.377 -0.269 -0.129 -0.217 -0.129 1.000

Early new phone -0.131 -0.171-0.160 -0.160 0.160 -0.077 -0.129 -0.077 -0.129 1.000

Late new phone 0.066 -0.026-0.236 0.236 0.236 -0.113 -0.190 -0.113 -0.190 -0.113 1.000

US GDP pvs quarter 0.355 0.387 0.020 -0.031 -0.008 0.001 -0.022 0.084 -0.128 0.043 -0.156 1.000

% Change in US Retail

Sales pvs quarter0.181 0.260-0.154 0.019 0.054 -0.034 0.111 -0.015 -0.328 0.025 -0.133 0.395 1.000

IDC smartphone sales

pvs quarter 0.992 0.955 0.097 0.078 -0.127 -0.052 -0.003 -0.147 0.201 -0.119 0.041 0.379 0.212 1.000

Apple market share pvs

quarter0.394 0.624 0.204 0.103 -0.338 0.388 -0.284 -0.084 0.179 -0.313 -0.021 0.048 0.248 0.458 1.000

Stock Price -0.207 -0.205-0.076 -0.275 0.305 -0.219 0.355 -0.337 -0.262 0.190 -0.123 0.022 0.538 -0.207 -0.207 1.000

13

MeanRegressors

• Overview & Background

• Full Model

• Best Model

• Predictions

• Conclusions

Agenda

14

MeanRegressors

Methodology: Going from the Full Model to the “Best” Model

Full Model

Best Subsets

9 Variable Model

8 Variable “Best”

Statistical Model

Multiplier Model (Most

Practical)

15

MeanRegressors

Best Subsets reveals a 9 Variable Model

Vars

R-

Sq

R-

Sq

(adj

)

R-Sq

(pred

)

Mallo

ws Cp S

iPhon

es

alread

y sold

Sales

last

quarte

r

2nd

Q

3rd

Q 4th Q

After

early

new

phon

e

After

late

new

phone

Before

early

new

phone

Before

late

new

phone

Early

new

phon

e

Late

new

phone

US

GDP

pvs

quarte

r

%

Change

in US

Retail

Sales

pvs

IDC

smartp

hone

sales

pvs

quarter

Apple

Market

share

pvs

Quarter

% One

quarter

lagging

stock

price1 85.2 84.6 82.2 94.7 6.1943 X

1 78.9 78.1 75.9 145.2 7.3871 X

2 89.9 89.1 87.2 58.8 5.2168 X X

2 87.4 86.5 80.3 78.5 5.8127 X X

3 92.7 91.8 89.3 37.9 4.5145 X X X

3 91.9 90.9 89.3 44.7 4.7679 X X X

4 94.8 93.9 90.2 23 3.8908 X X X X

4 93.8 92.8 90.4 31 4.2472 X X X X

5 96.1 95.3 92.5 14.1 3.422 X X X X X X

5 95.3 94.3 91.1 21.1 3.7863 X X X X X

6 96.9 96.1 94.1 9.7 3.1155 X X X X X X X

6 96.8 95.9 93.6 10.9 3.1942 X X X X X X X

7 97.3 96.5 94.6 8.5 2.9735 X X X X X X X

7 97.3 96.4 94.5 8.7 2.9914 X X X X X X X X

8 97.9 97.1 95.3 5.8 2.6982 X X X X X X X X

8 97.5 96.4 94.4 9.6 2.9851 X X X X X X X X X

9 98.1 97.2 95.4 6.6 2.6661 X X X X X X X X X

9 98 97.1 95.2 7 2.7035 X X X X X X X X X

10 98.2 97.2 95.4 7.5 2.638 X X X X X X X X X X

10 98.1 97.1 95 8 2.6837 X X X X X X X X X X

11 98.3 97.2 95 8.8 2.6477 X X X X X X X X X X X

11 98.3 97.2 95.1 8.8 2.6519 X X X X X X X X X X X

12 98.4 97.2 94.9 10.1 2.6644 X X X X X X X X X X X X

12 98.4 97.1 95.1 10.3 2.6814 X X X X X X X X X X X X

13 98.5 97.1 93.2 11.7 2.7083 X X X X X X X X X X X X X

13 98.5 97.1 94.5 11.7 2.7104 X X X X X X X X X X X X X

14 98.5 97 94.1 13.2 2.7447 X X X X X X X X X X X X X

14 98.5 97 92.8 13.3 2.7564 X X X X X X X X X X X X X X X

15 98.5 96.8 92.2 15 2.8281 X X X X X X X X X X X X X X

15 98.5 98.8 93.1 15.2 2.8466 X X X X X X X X X X X X X X X

16 98.5 96.5 91 17 2.942 X X X X X X X X X X X X X X X X

16

MeanRegressors

However, the 9 Variable Model had Significant Correlation issues

iPhones

already sold

Sales last

quarter 2nd Q 3rd Q 4th Q

After late

new phone

Early

new

phone

Late

new

phone

IDC

smartphone

sales pvs

quarter

iPhones already

sold 1

Sales last quarter 0.929198 1

2nd Q 0.056063 0.221983 1

3rd Q 0.055457 0.033303 -0.34816 1

4th Q -0.08441 -0.16728 -0.31818 -0.34816 1

After late new

phone 0.029775 -0.08426 -0.25746 -0.28172 0.382518 1

Early new phone -0.11978 -0.15539 -0.15352 -0.16798 0.164488 -0.12423 1

Late new phone -0.01342 -0.11225 -0.25746 0.331019 0.169191 -0.20833 -0.12423 1

IDC smartphone

sales pvs quarter 0.991943 0.956465 0.115687 0.011013 -0.1026 0.014815 -0.10558 -0.04701 1

17

MeanRegressors

So we moved to an 8 Variable “Best” Regression Model

Regression Statistics

Multiple R 0.989533

R Square 0.979175

Adjusted R Square 0.970845

Standard Error 2.698235

Observations 29

ANOVA

df SS MS F Significance F

Regression 8 6846.501 855.8126 117.5491 4.14E-15

Residual 20 145.6094 7.280469

Total 28 6992.111

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -7.82482 2.098311 -3.7291 0.001324 -12.2018 -3.44782

iPhones already

sold -0.19082 0.029909 -6.38005 3.17E-06 -0.25321 -0.12843

2nd Q -5.12848 1.660849 -3.08787 0.005802 -8.59295 -1.66401

3rd Q -3.87366 1.607004 -2.41048 0.025676 -7.22581 -0.5215

4th Q -7.76355 1.561421 -4.9721 7.33E-05 -11.0206 -4.50648

After late new

phone 9.144095 1.694359 5.396786 2.78E-05 5.609724 12.67847

Early new phone 9.502097 2.243513 4.235365 0.000406 4.82221 14.18198

Late new phone 3.715057 1.583681 2.345837 0.029405 0.411557 7.018557

IDC smartphone

sales pvs quarter 1.177552 0.125415 9.389252 9.03E-09 0.915941 1.439163

SALES = 2.77 + 0.618 Sales last quarter + 0.0614 IDC smartphone sales pvs quarte

+ 0.0 2nd Q_0 - 4.07 2nd Q_1 + 0.0 3rd Q_0 - 7.28 3rd Q_1 + 0.0 4th Q_0

- 9.76 4th Q_1 + 0.0 After late new phone_0 + 11.25 After late new phone_1

+ 0.0 Early new phone_0 + 13.93 Early new phone_1 + 0.0 Late new phone_0

+ 5.62 Late new phone_1

18

MeanRegressors

The Residuals looked pretty good in the 8 Variable Model

19

MeanRegressors

And the fit of this model to the data is very strong

-10

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Sale

s (

in m

illio

ns)

Time

Sales: Model Prediction vs. Actual

Model Predicted Sales Actual Sales

20

MeanRegressors

Does the model make sense?

-10

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Sale

s (

in m

illio

ns)

Time

Sales: Model Prediction vs. Actual

Model Predicted Sales Actual Sales

Might be true at some points, but not generally

Examples

• If it’s the fourth quarter, subtract

7.7M iPhones

• If a new iPhone was launched late in

the last quarter, add 9.1M iPhones

21

MeanRegressors

• Exponential model

• Holt-Winters model

• Something else

Possible alternatives:

22

MeanRegressors

Additive Holt-Winters

Method we learned in class. Seasons add/subtract to sales

0.00

10.00

20.00

30.00

40.00

50.00

60.00

Q3 '0

7

Q4 '0

7

Q1 '0

8

Q2 '0

8

Q3 '0

8

Q4 '0

8

Q1 '0

9

Q2 '0

9

Q3 '0

9

Q4 '0

9

Q1 '1

0

Q2 '1

0

Q3 '1

0

Q4 '1

0

Q1 '1

1

Q2 '1

1

Q3 '1

1

Q4 '1

1

Q1 '1

2

Q2 '1

2

Q3 '1

2

Q4 '1

2

Q1 '1

3

Q2 '1

3

Q3 '1

3

Q4 '1

3

Q1 '1

4

Q2 '1

4

Q3' 1

4

Sales

Forecast

23

MeanRegressors

Seasons multiply sales instead of adding/subtracting from them

Multiplicative Holt-Winters

0

10

20

30

40

50

60Q

3 '0

7

Q4 '0

7

Q1 '0

8

Q2 '0

8

Q3 '0

8

Q4 '0

8

Q1 '0

9

Q2 '0

9

Q3 '0

9

Q4 '0

9

Q1 '1

0

Q2 '1

0

Q3 '1

0

Q4 '1

0

Q1 '1

1

Q2 '1

1

Q3 '1

1

Q4 '1

1

Q1 '1

2

Q2 '1

2

Q3 '1

2

Q4 '1

2

Q1 '1

3

Q2 '1

3

Q3 '1

3

Q4 '1

3

Q1 '1

4

Q2 '1

4

Q3' 1

4

Forecast

Sales

24

MeanRegressors

Uses Solver-derived multipliers for iPhone launch variables

Multiplicative Holt-Winters with iPhone cycle adjustment

0.00

10.00

20.00

30.00

40.00

50.00

60.00Q

3 '0

7

Q4 '0

7

Q1 '0

8

Q2 '0

8

Q3 '0

8

Q4 '0

8

Q1 '0

9

Q2 '0

9

Q3 '0

9

Q4 '0

9

Q1 '1

0

Q2 '1

0

Q3 '1

0

Q4 '1

0

Q1 '1

1

Q2 '1

1

Q3 '1

1

Q4 '1

1

Q1 '1

2

Q2 '1

2

Q3 '1

2

Q4 '1

2

Q1 '1

3

Q2 '1

3

Q3 '1

3

Q4 '1

3

Q1 '1

4

Q2 '1

4

Q3' 1

4

Q4' 1

4

Sales

Forecast

25

MeanRegressors

Weakness: poor predictions

If you don’t have access to full dataset, errors are big

Quarter Prediction Actual Error

Q3 '13 31.24 31.24 0%

Q4 '13 26.41 33.8 28%

Q1 '14 57.76 51.03 12%

Q2 '14 49.22 47.03 11%

Q3 '14 34.96 35.2 0.70%

26

MeanRegressors

Solution: Model that combines best features of Winters and regression

■ Replaces seasonal dummy variables with multiples of average sales for last year

■ Detail of dataset fed into regression:

1st Q 2nd Q 3rd Q 4th QAfter early

new phone

After late

new phone

Before late

new phone

Early new

phone

Multiplier =

average of

last year's

quarterly

sales

0 - - - - - - - 0.00

0 - - 0.27 - 0.27 - - 0.27

0.695 - - - - - - - 0.70

0 1.24 - - - - - - 1.24

0 - 1.35 - - - - - 1.35

0 - - 1.47 - - - 1.47 1.47

2.9075 - - - 2.91 - - - 2.91

0 3.42 - - - - 3.42 - 3.42

0 - 3.94 - - - - - 3.94

0 - - 5.06 - 5.06 - - 5.06

27

MeanRegressors

A good fit, and one that makes sense

■Adjusted R2 of 0.983

■Take the average sales for the last year. Multiply by seasonal factor to get A, multiply by iPhone cycle factor to get B. Predicted sales = A+B

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Predicted SALES

Actual

28

MeanRegressors

• Overview & Background

• Full Model

• Best Model

• Predictions

• Conclusions

Agenda

29

MeanRegressors

Prediction quality

Quarter Regular

regression

Winters-Holt w/

iPhone cycle

Multiplier

regression

Prediction Error Prediction Error Prediction Error

4-2013 41.6 23.0% 26.41 28% 33.9 0.2%

1-2014 56.3 10.3% 57.76 12% 57.8 13.2%

2-2014 46.8 7.0% 49.22 11% 43.9 0.4%

3-2014 38.5 9.3% 34.96 0.70% 36.5 3.6%

Average error 12.4% 12.9% 4.4%4.4%

30

MeanRegressors

Prediction for the latest quarter

Regular

regression

Winters-Holt w/

iPhone cycle

Multiplier

regression

33.8 +/- 2.7M 34.9M 38.4 +/- 2.1M

■Sales for July to September to be reported Oct. 20 – in one week

38.4 +/- 2.1M

36.3-40.5 million iPhones sold

31

MeanRegressors

• Overview & Background

• Full Model

• Best Model

• Predictions

• Conclusions

Agenda

32

MeanRegressors

Our model turned out very strong, but not without some very notable limitations.

Use of past data

Potential over-fitting

(Adjusted R2: 0.982)

Lack of MECE in model

33

MeanRegressors

Our model will predict strong growth. However, we should be cognizant that technology performance runs on an S-curve.

Pro

du

ct

Pe

rfo

rma

nce

Time

Prediction

Reality

34

MeanRegressors

In summary, Apple has a competitive brand and loyal consumers. Also, use logic to supplement regression models.

■ iPhone demand is inelastic

■Apple has strong and surprisingly predictable growth (so far!)

■Regression models are great, but use with caution

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