Interpret logistic regression output from Minitab

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Interpret logistic regression output from Minitab	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Logistic regression: interpretation of software output.	Ready to use	Mario Orsi	17/05/2023 10:13

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Question statement

It is claimed that there is a relationship between job type and obesity, with employees in more highly-paid, senior roles being more likely to be overweight than those in other roles.

You are an analyst working for a large company and have been given the task to see if this is the case at your workplace.

You randomly sample 15 employees and record their annual salary ( $X$ , in thousands of pounds) and whether or not they are obese (have a body mass index of more than 30: $Y=1$ if yes, $Y=0$ if no).

A logistic regression was performed in Minitab, with the following (edited) output shown below:

					Odds	95% CI
Predictor	Coef	SE Coef	Z	P	Ratio	Lower	Upper
Constant	$A$	{sea}	-2.24	0.025
$x$	$B$	{seb}	2.25	0.025	1.18	1.02	1.37

Give any introductory information the student needs.

			Name	Type	Generated Value

seb	number	0.107317
r1	number	0.706
tol1	number	0.01
v1	number	2.426827
v2	number	4.226827
t	integer	67
tol	number	0.001
ansa	number	-6.765
ansb	number	0.241
thismuch	integer	31000
sea	rational	151/50
prob1	number	0.67

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.04..1.2#0.000001)

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`

0.107317

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Find $A$ and $B$ each to 3 decimal places:

$A=\;$ Gap 0. $B=\;$ Gap 1.

Advice

A is given by A = -2.24 x SE Coef (A) = -2.24 x {sea} = {ansa} .

B is given by B = 2.25 x SE Coef (B) = 2.25 x {seb} = {ansb} .

Both to 3 decimal places.

The probability is given by:

$\begin{align}P(Y=1 | X=\var{thismuch})&=\frac{e^{A+B\times\var{thismuch/1000}}}{1+e^{A+B\times\var{thismuch/1000}}}\\&=\frac{e^{\var{r1}}}{1+e^{\var{r1}}}=\var{prob1}\end{align}$

to 2 decimal places.

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Interpret logistic regression output from Minitab

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Taxonomy: mathcentre

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History

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Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Interpret logistic regression output from Minitab

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`