MGTSC 312: Lab 9

November 24, 2011 - Transformations

Announcements

• Hw 7 is due this

Friday at 11:59 p.m. DO NOT SUBMIT LATE!

• Hw 8 is due on

December 6 at 11:59 p.m. DO NOT SUBMIT LATE!

• Lab Exam 3 is next Thursday December 1 -For coverage please see the Exam 3 materials link under “Exams and Quizzes”

MGTSC 312: Lab 9 - Loglinear Model 2

Agenda

• Evaluation Survey • Today’s lab relates to Topic 10 ‒ GDP data ‒ Linear Model ‒ Loglinear Model • Memo Formatting

MGTSC 312: Lab 9 - Loglinear Model 3

Look at the Data

• • • • • Canadian Gross Domestic Product (GDP) ‒ Quarterly from 1961Q1 to 1989Q4 Use the graph wizard to create a scattergraph Does the graph look like a straight line?

Is there any repeating pattern?

Add a linear trendline and an exponential trendline ‒ ‒ The exponential looks like a much better fit The exponential corresponds to regressing the natural logarithm of GDP on Time, which is what we’re about to do

MGTSC 312: Lab 9 - Loglinear Model 4

Transform the Data

• • • • • • Let’s create a new dependent variable for a regression, the natural log of GDP Use Excel’s

=LN()

function Create a line graph for LnGDP vs. year/quarter Does it look like a straight line?

Change the y-axis scale to use all of the available space!

We also need to change the time to just numbers, starting at 1 and counting by 1 to 116 (which is just Obs #)

MGTSC 312: Lab 9 - Loglinear Model 5

Regress GDP and lnGDP on Time

• Insert a new ‘Regress’ worksheet for the output • Regress lnGDP the same way and put the output beside the first ‒ R 2 and F test comparable are even larger, but the scale is different so R 2 is not

MGTSC 312: Lab 9 - Loglinear Model 6

Find the Growth Factor and Rate

• • • The quarterly growth factor is EXP(b 1 ) = 1.0268

The annual growth factor is the quarterly growth factor to the power of 4 = 1.1116

• The quarterly growth rate as a percent ‒ 100*(quarterly growth factor - 1) = 2.68% The annual growth rate as a percent ‒ 100*(annual growth factor - 1) = 11.16% • On average GDP increased by about 11.16% per year from 1961 through 1989 – looks pretty large compared to the last year!

7 MGTSC 312: Lab 9 - Loglinear Model

Predicted GDP from Loglinear

• Copy the Predicted lnGDP from the loglinear regression and paste to another sheet • Calculate the predicted GDP as

=EXP(predicted lnGDP)

• Beside that column, copy and paste the predicted GDP from the linear model (Note the negative values!) • Beside that column, copy and paste the actual GDP

MGTSC 312: Lab 9 - Loglinear Model 8

Predicted GDP and Actual

MGTSC 312: Lab 9 - Loglinear Model lnPredict exp(lnPred)[y^] actual

9.12

9164.8

9290 9.15

9.18

9.20

9.23

9.26

9.28

9.31

9.33

9.36

9.39

9.41

9.44

9.47

9.49

9.52

9.55

9.57

9.60

9410.4

9662.7

9921.7

10187.7

10460.8

10741.2

11029.1

11324.7

11628.3

11940.0

12260.1

12588.7

12926.2

13272.6

13628.4

13993.8

14368.9

14754.0

10008 11148 10727 10053 10719 12396 11497 10714 11468 13270 12509 11938 12654 14395 13562 12928 13881 15889

9

Plot Both Predicted versus Actual

• Loglinear is a much better fit for the data

MGTSC 312: Lab 9 - Loglinear Model 10

Does Quarter Add Anything?

• If there’s time, let’s see whether the quarter of the year makes a difference • • • Add Quarter with =VALUE(RIGHT(B2,1)) Add quarter dummies with =IF() as we’ve done previously Regress lnGDP on Time and three quarter dummies ‒ Two of the quarter dummies have p-values < 0.01

• Perform a Partial F test ‒ p-value = 1.1E-7 ‒ The quarter dummies improve the fit, so use all 3

11 MGTSC 312: Lab 9 - Loglinear Model

Does Quarter Add Anything?

Regression Statistics Multiple R 0.997

Time & Quarter

R Square Adjusted R Square Standard Error 0.994

0.994

0.071

Observations 116 ANOVA Regression Residual Total df 4 111 115 SS 91.222

0.562

91.784

MS F 22.805 4501.506

0.005

Reduced

Regression

Partial F

SSR-SSR dfR - dfR Fnum Fden Ftest dfDen p-value Intercept Time Q1 Q2 Q3 Coeff 9.103

0.026

-0.057

-0.021

0.060

Std Error 0.018

0.000

0.019

0.019

0.019

t Stat P-value 512.812 3.8E-189 133.816 1.6E-124 -3.044 0.002913

-1.099 0.274192

3.223 0.001668

MGTSC 312: Lab 9 - Loglinear Model

df 1 SS 91.013

0.2092

3 0.0697

0.0051

13.7659

111 1.072E-07

12

Memo Formatting

Memo Formatting

• The first part of the file tells you how to format the HW 8 file, but doesn’t follow its own instructions • Let’s make the file follow the rules • There are often several ways to accomplish the same task in Word; use your favourite • If the rulers are not visible go to View > Show/Hide > Ruler and drag the margin markers ‒ Or go to Page Layout > Margins • Home > Select > Select All ‒ Font Times New Roman 11 pt ‒ Paragraph > Spacing: Single, Before (or After) 6 pts, or 3 pts before and 3 pts after. Ensure the “Don’t Add Space…” box remains unchecked • Grammar and Spell checking ‒ Office button > Word Options > Proofing • Office button > Save As > Word ‘97 – 2003 document

MGTSC 312: Lab 9 – Loglinear Model 14