Logistic regression: interpretation of software output.

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Mario Orsi

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Created this as a copy of Interpret logistic regression output from Minitab.

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 hypothesized that there is a relationship between salary and obesity, with employees in more highly-paid roles being more likely to be overweight than those in other roles.

To test this hypothesis, the following data are collected for a random sample of 15 employees:

their annual salary ( $x$ , in thousands of pounds);
whether or not they are obese $\Rightarrow$ body mass index of more than 30: $Y=1$ if yes, $Y=0$ if no.

A logistic regression is performed using statistical software, obtaining the following (edited) output:

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

Give any introductory information the student needs.

			Name	Type	Generated Value

seb	number	0.880
r1	number	-0.66
v1	number	14.94
v2	number	16.74
t	integer	29
tol	number	0.2
ansa	number	-36.3
ansb	number	1.98
thismuch	integer	18
sea	number	16.2
prob1	number	0.341

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
siground(random(0.04..1.2#0.000001),3)

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`

0.880

→ Used by:

ansb
v1
v2

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 $B$ :

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

Advice

Revise logistic regression, e.g., Section 9.5 of OpenIntro Statistics.

Use the Z-score definition ( $Z=\frac{x-\mu_0}{SE}$ , with $\mu_0=0$ ) and solve for $x$ :

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}.

The probability is given by:

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

If using a spreadsheet program (e.g., Excel), note that $e^x$ corresponds to EXP( $x$ ).

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

This question is used in the following exams:

Exam May 2021 by Mario Orsi in Stats.
Sarah's copy of Exam May 2021 by Sarah Dean in Applied Scientific Practice.
CL2603- Multiple Regression and Logistic Regression by Ben Parker in Ben's workspace.
SPtest2 by Mario Orsi in Trash-backup.
ResitExam20Qs by Mario Orsi in Stats.
ResitExam by Mario Orsi in Stats.
SP test 2 by Mario Orsi in Stats.

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Logistic regression: interpretation of software output.

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Mario Orsi 5 years, 1 month ago

Mario Orsi 5 years, 1 month ago

Mario Orsi 5 years, 1 month ago

Error in variable testing condition

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Generated value: `number`

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Gap-fill

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Logistic regression: interpretation of software output.

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mario Orsi 5 years, 1 month ago

Mario Orsi 5 years, 1 month ago

Mario Orsi 5 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`