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<= /td> TEST 2 KEY FALL 2007
POPULATION SALES A)
(1000's) ($1,000)
<= /td>
106 2607
96 2099
108 2945
49 1050
72 1266
52 883
54 1647
70 1841
51 1908
79 2130
110 2688
110 2703
<= /td>
<= /td>
F)
NULL: THE MODEL IS NOT SIGNIFICANT
ALTERNATIVE: THE MODEL IS BEST FIT IS MEASURED BY THE = LEAST SQUARES CRITERION WHICH
SIGNIFICANT MINIMIZES THE DISTANCE THE P= OINTS ARE OFF THE LINE
=
F TEST
=
FCAL =3D 34.03828= 729 SUMMARY OUTPUT
FCRIT =3D 4.964602701
SINCE FCAL > FCRIT REJECT THE NULL = Regression Statistics
T= HE MODEL IS SIGNIFICANT Multiple R 0.879161
<= /td> R Square 0.772925
P TEST Adjusted R Square 0.750217
PCAL =3D 0.000= 165099 Standard Error 340.2563
PCRIT =3D 0.05 Observations 12
S= INCE PCAL < PRCIT REJECT THE NULL
TH= E MODEL IS SIGNIFICANT ANOVA
<= /td>   df SS MS F Significance F
THERE IS A SIGNIFICANT LINEAR  Regression 1 3940760 3940760 34.03829 0.000165
R= ELATIONSHIP BETWEEN POPULATION Residual 10 1157743 115774.3
AN= D SALES. Total 11 5098503      
<= /td>
G)   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
NULL:BETA 1 IS 0 Intercept 80.50921 340.1664 0.236676 0.817686 -677.429 838.4472 -677.429 838.4472
ALTERNATIVE: BETA 1 IS NOT 0 X Variable 1 23.82538 4.08372 5.834234 0.000165 14.72628 32.92448 14.72628 32.92448
=
T TEST
=
TCAL =3D 5.834234= 079 RESIDUAL OUTPUT B) R SQUARED =3D 0.77292= 5
TCRIT =3D 2.228138842 THIS MEANS THAT 77.3% OF THE VARIATION IN SALES
S= INCE TCAL > TCRIT REJECT THE NULL Observation Predicted Y Residuals IS EXPLAINED BY THE VARIATION IN POPULATION
B= ETA 1 IS NOT ZERO 1 2606 1.00042
<= /td> 2 2367.746 -268.746 C) RESIDUAL STANDARD ERROR IS = =3D 340.2563=
P TEST 3 2653.65 291.3497 THE PROBLEM IS THAT THIS APPROXIMATION OF THE
PCAL =3D 0.0001= 65099 4 1247.953 -197.953 POPULATION STANDARD DEVIATIO= N IS RELATIVE SO
PCRIT =3D  0.05 5 1795.937 -529.937 WE HAVE NO GOOD IDEA HOW GOO= D OR BAD IT IS
S= INCE PCAL < PRCIT REJECT THE NULL 6 1319.429 -436.429
B= ETA 1 IS NOT ZERO 7 1367.08 279.9202 D) THE FITTED REGRESSION MODEL = IS
<= /td> 8 1748.286 92.71413
THERE IS A SIGNIFICANT LINEAR  9 1295.604 612.3964 SALES =3D 80.50921= +' 23.82538<= /td> POPULATION
RELATIONSHIP BETWEEN POPUL= ATION AND  10 1962.714 167.2857
SALES. 11 2701.301 -13.3011 E) THE INTERCEPT IS 80.50921=
12 2701.301 1.698897 THIS MEANS WHEN POPULATION I= S ZERO SALES WILL
H) BE $80509.21.
C= ONFIDENCE INTERVAL BUILT AROUND
B= ETA 1 (THE SLOPE) THE SLOPE IS 23.82538<= /td>
<= /td> THIS MEANS FOR EACH ADDITION= AL 1000 POPULATION
BETA 1 =3D 23.82538<= /td> SALES WILL INCREASE BY $2382= 5.38.
T =3D 2.228139=
S= E(BETA 1) =3D 4.08372<= /td> I) residuals vs fitted
<= /td>
LOWER = 14.72628
UPPER = 32.92448
Z= ERO IS NOT IN INTERVAL, REJECT THE NULL
T= HAT BETA 1 IS 0.  IN FACT NOW WE CAN SA= Y
T= HAT WE ARE 95% CONFIDENT THAT THE TRUE
P= OPULATION SLOPE IS BETWEEN 14.72 AND 32,92.
T= HERE IS A SIGNIFICAN POSITIVE RELATIONSHIP
B= ETWEEN POPULATION AND SALES.
<= /td>
<= /td>
<= /td>
<= /td>
<= /td>
<= /td>
<= /td>
<= /td>
<= /td>
<= /td> LOOKING FOR RANDOM, SEE NO DISTINGUISHABLE PATTERN, ONLY 3 NEGATIVE POINTS
<= /td> MAY BE DUE TO ONLY 12 POINTS=
I) cont actual vs predicted
=
= =
histogram of residuals
=
<= /td> min -529.937
<= /td> max 612.3964
<= /td> range 1142= .333
<= /td> width 228.46= 66
=
<= /td> start end frequency
<= /td> -529.93= 7 = -301.47 2
<= /td> -301.4= 7 = -73.0034 2
<= /td> -73.00= 34 1= 55.4632 4
<= /td> 155.463= 2 3= 83.9298 3
<= /td> 383.929= 8 612.3964= 1
=
l= ooking for a straight line , this looks good
<= /td>
EXTRA CREDIT
=
XSTAR 6200 (SHOULD HAVE BEEN 62000 BUT = A ZERO
<= /td> WAS MISSING ON TEST)
6.2
XBAR 79.75
=
X= STAR -XBAR -73.55
=
X X-XBAR SQUARED
106 26.25 689.0625
96 16.25 264.0625
108 28.25 798.0625
49 -30.75 945.5625 looking for normal, this is approximately normal
72 -7.75 60.0625
52 -27.75 770.0625
54 -25.75 663.0625
70 -9.75 95.0625
51 -28.75 826.5625
79 -0.75 0.5625
110 30.25 915.0625
110 30.25 915.0625 SE(MEAN RESPONSE)  316.0104
=
SUM 0 6942.25 T 2.228139
=
<= /td> YHAT 228.2266
=
<= /td> LOWER -475.888
<= /td> UPPER 932.3416
<= /td> WITH 95% CONFIDENCE WE CAN S= AY THAT
<= /td> A POPULATION OF 6200 WILL Y= IELD BETWEEN A SALES LOSS OF($475,000) AND SALES OF $932.34
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