How to Interprete the Minitab Output of a Regression Analysis

7/25/2019 How to Interprete the Minitab Output of a Regression Analysis

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How to interpret a minitab output of a regression analysis

Step I:Model: From the description of the problem, it says that this a time series data where the weight of soa

depends on the number of days it had been used. Thus dependent variable(y) is weight of the soap and

independent variable is the number of days (x).e wish to fit a liner model ! " # $ %x

Step II:The following scatter diagram shows that

&. there is a inverse relationship between x and y, that is as the number of days increase, weight of

soap decreases.

'. e see a distinct liner trend among the data points supporting our model in step .

Day

Weight

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140

120

100

80

60

40

20

0

Scatterplot of Weight vs Day

. *earson correlation of +ay and eight " -./*0alue " -.---. This tells us that the sample estimates of *earson correlation of +ay and

eight is -./ based on &1 observations. hen test for significance, a low pvalue re2ects

the null that rho"- and we conclude that the sample estimates 2ust did not come from thenoise. There is a meaningful linear relationship between the two variables.

Step III & IV:

Estimates and evaluation:e estimate the model using least s3uare method. The computation from the minitab is as follows:The regression equation is

Weight = 123 - 5.57 Day

Interpretation: the line intersects y axis at 123 with a slope of -5.57. that is on the ay!"#

weight is 123gm an for each increase in a ay# the weight of the soap ecreases on the

a$erage by 5.57 grams.


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Predictor Coef S Coef T P

Constant 123.1!1 1.3"2 "#.$# $.$$$

Day -5.57!" $.1$%" -52.1# $.$$$

Interpretation: the sample estimates of alpha an beta are 123.1%1 an -5.57

respecti$ely. &he corresponing test statistics are '(."( an -52.1" inicating that these

are too large $alues of t-statististics an lie on the extreme ens of t-cur$e.

&hus we re)ect the null hypothesis of alpha !o an beta!o. *n conclue that the betaan alpha play a significant role in the regression moel.

S = 2.#!#21 &-Sq = ##.5' &-Sq(ad)* = ##.5'

Interpretation: the stanar e$iation of the error terms is 2.(%. * ((.5+ ,-sa)

inicates that when e$er we obser$e a $ariation in the $alue of y# ((.5+ of it is ue to

the moel or ue to change in x/ an only .5+ is ue error or some unexplaine factor.

&hat is this ata fits well to the linear moel.

+na,ysis of ariance

Source D SS /S P

&egression 1 23%#! 23%#! 272!.11 $.$$$&esidua, rror 13 113 #

Tota, 1! 23"$7

Interpretation: In this case *0* tests the hypothesis that beta!". In fact is nothing

but &-suare. * low p-$alue suggest that beta plays a significant role in the moel# this is

)ust reassurance of the t-test.0nusua, serations

s Day Weight it S it &esidua, St &esid

1$ 12.$ 5$.$$$ 5%.2!! $.772 -%.2!! -2.1#&

15 22.$ %.$$$ $.!#% 1.!1" 5.5$! 2.13&

& denotes an oseration 4ith a ,arge standardied residua,.

Interpretation: the obser$ation number 1" an number 15 are outliers. 4e nee to go

bac an re$iew what happene on those ays # either soap is use too much or too less.

&o impro$e the moel# we woul lie to elete those obser$ation an recompute the

line.

tep 5:

6hecing the $aliity of the assumptions:

4e mae the assumptions that the all the error terms are ientically an inepenently

normally istribute with mean " an common $ariance sigma suare.


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Residual

Percent

5.02.50.0-2.5-5.0

99

90

50

10

1

Fitted Value

Residual

1209060300

5.0

2.5

0.0

-2.5

-5.0

Residual

Frequency

6420-2-4-6

6.0

4.5

3.0

1.5

0.0

Observation Order

Residual

151413121110987654321

5.0

2.5

0.0

-2.5

-5.0

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

istogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Weight

Interpretation:

1. the graph on top left checs the assumption of normality of error terms. In this

case we see that most of the points are clustere aroun blue line inication that

the error terms are approximately normal. &hus our assumption of normality is

$ali.2. &he graph on top right plots the error terms against the fitte $alues. &here are

approximately half of them are abo$e an half are below the 8ero line inicating

that our assumption of error terms ha$ing mean 8ero is $ali.

3. n the same graph we see the clear cyclic pattern among the error terms

inicating that they are $iolating the assumption of inepenence of error. 9rror

terms are not inepenent. ay be there is another factor present in this

example which we nee to fin out.

%. &he bottom left graph again re-emphasi8es the normality assumption. &hough

our sample si8e is )ust 15.

5. &he bottom right graph is also important in this case because ata is a time

series an orer of the ata is important. * clear cyclic pattern inicates thaterror terms are epenent on the time $ariable.

Step VI:*lthough the beta is significant an , s a) is $ery high inicating that moel is a $ery

goo fit to the ata# there is $iolation of assumption of inepenence inicate that there

is some other factor which is playing role behin the screen an we may ha$e to stuy it

further.

Step VII:;et us estimate the $alue of y an interpret it t = .'%%1 ! %5."2> 2.32?=.'%%1! %3."5?5# %?.(?35/


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4e are ('+ confiant that that on the 1% th ay the weight of the soap on the a$erage

lies between %3 grams an %7 grams approx.

('+ preiction inter$al:

%5."2> 2.32?= 3.11?3 ! %1.("3?# %'.13?3/

4e are ('+ confiant that on the 1%thay the preicte $alueof the weight of thesoap lies between 42 grams and 48 grams approx.

2520151050

S 2.94921

R-Sq 99.5%

R-Sq(adj) 99.5%

Regression

95% CI

95% I

Fitted !ine Plot!eig"# $ 123.1 - 5.575 a&

(optional)For those who want to improve upon the model4uadratic fitting: compare the svalue and 5s3 ad2 value with last model.


5/5

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S 1.95599

R-Sq 99.8%

R-Sq(adj) 99.8%

Regression

95% CI95% I

Fitted !ine Plot!eig"# $ 127.3 - 6.744 a&

' 0.05063 a&2

0alidation of assumptions in 3uadratic fitting:

Residual

Percent

5.02.50.0-2.5-5.0

99

90

50

10

1

Fitted Value

Residual

1209060300

2

0

-2

-4

Residual

Frequen

cy

3210-1-2-3-4

4

3

2

1

0

Observation Order

Residual

151413121110987654321

2

0

-2

-4

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

istogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Weight

(5 denotes an observation with a large standardi6ed residual)

How to Interprete the Minitab Output of a Regression Analysis

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