Interpret Minitab output of multiple regression

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

Name	Status	Author	Last Modified
Interpret Minitab output of multiple regression	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Multiple regression - interpretation of software analysis	Ready to use	Mario Orsi	16/03/2021 15:25

Question statement

The management at {thisrest} propose the following model to predict sales Y at their {place} branch.

$Y = \beta_0+ \beta_1 X_1 + \beta_2 X_2 + \beta_3X_3 + \epsilon$

where

$X_1=\;$ number of competitors within one kilometre.

$X_2=\;$ population within one kilometre (in 1000s).

$X_3=\;$ 1 if {cond}, 0 otherwise.

Give any introductory information the student needs.

			Name	Type	Generated Value

cb	number	-0.3607
sed	number	1.192
cond	string	has got a drive-thru window
sea	number	3.696
ind	integer	5
pred	number	16.8
sval	number	0.312769
tol	number	0.001
thisrest	string	Pacino's Italian Restaurant
thismany	integer	9000
ansa	number	14.366
ansb	number	0.137
ansc	number	0.172
ansd	number	3.016
thatmany	integer	6
sv	list	List of 6 items
hascond	string	has got a drive-thru window
q	integer	1
p	integer	0
si	number	0.098
place	string	Alnwick
se	number	0.0451

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-0.5..-0.1#0.0001)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

-0.3607

This variable doesn't seem to be used anywhere.

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Ask the student a question, and give any hints about how they should answer this part.

Which of these variables is an indicator variable?

Unnamed gap

Advice

a) $X_3$ is the indicator variable.

(i) The values of A, B, C and D are given by:

A = 3.887 x SE Coef (A) = 3.887 x {sea} = {ansa} to 3 decimal places.

B = Coef (B)/-2.64 = {cb}/-2.64 = {ansb} to 3 decimal places.

C = 3.82 x SE Coef (C) = 3.82 x {se} = {ansc} to 3 decimal places.

D = 2.53 x SE Coef (D) = 2.53 x {sed} = {ansd} to 3 decimal places.

ii) The fitted regression equation is:

$Y=\var{ansa}-\var{abs(cb)}X_1+\var{ansc}X_2+\var{ansd}X_3+\epsilon$ with

$\sigma^2=\var{sval}^2=\var{si}$ all to 3 decimal places.

Using the above fitted model where $X_1=\var{thatmany}$ and $X_2= \frac{\var{thismany}}{1000}=\var{thismany/1000}$ and since $X_3=\var{q}$ as the restaurant {hascond} we find :

$Y=\var{ansa}-\var{abs(cb)}\times \var{thatmany}+\var{ansc}\times \var{thismany/1000}+\var{ansd}\times \var{q}=\var{pred}$ to one decimal place.

There are {ind} categories in the survey and so the number of indicator variables is {ind}-1={ind-1}.

Give a worked solution to the whole question.

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Interpret Minitab output of multiple regression

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

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Interpret Minitab output of multiple regression

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`