Linear regression and correlation - pub sales

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Created this as a copy of Find regression equation and correlation coefficient, .

Name	Status	Author	Last Modified
Find regression equation and correlation coefficient,	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Linear regression and correlation - pub sales	Ready to use	Mario Orsi	16/02/2021 17:59

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Question statement

{owner['name']} owns the {pub}; {owner['pronouns']['they']} believes that sales of {beverage} in the pub are linked to the average monthly temperature, with higher sales being recorded in months with higher temperatures. To investigate, {owner['name']} records the average monthly temperature in the local town over a period of one year ( $x$ , in units of $^\circ$ C), along with total monthly sales of {beverage} ( $y$ , in units of £1000). The results are shown in the table below:

Month	x	y
{obj[0]}	{r1[0]}	{r2[0]}
{obj[1]}	{r1[1]}	{r2[1]}
{obj[2]}	{r1[2]}	{r2[2]}
{obj[3]}	{r1[3]}	{r2[3]}
{obj[4]}	{r1[4]}	{r2[4]}
{obj[5]}	{r1[5]}	{r2[5]}
{obj[6]}	{r1[6]}	{r2[6]}
{obj[7]}	{r1[7]}	{r2[7]}
{obj[8]}	{r1[8]}	{r2[8]}
{obj[9]}	{r1[9]}	{r2[9]}
{obj[10]}	{r1[10]}	{r2[10]}
{obj[11]}	{r1[11]}	{r2[11]}

Give any introductory information the student needs.

			Name	Type	Generated Value

ch	integer	9
prediction	integer	19
b	number	0.35
owner	dict	Dictionary with 3 entries
sxy	number	2586
res	list	List of 12 items
spxy	number	42
ls	number	18.10
tol	number	0.05
tcorr	number	0.109944128
b0	number	16.4
ssq	list	[ 2126, 4112 ]
sumr	number	489.275
pub	string	Black Bull Inn
a	integer	11
thisval	integer	20
corr	number	0.110
tsqovern	list	[ 1728, 3745.3333333333 ]
b1	number	0.106
obj	list	List of 12 items
r1	list	List of 12 items
r2	list	List of 12 items
ss	list	[ 398, 366.6666666667 ]
n	integer	12
beverage	string	ice-filtered cider
t	list	[ 144, 212 ]
sc	integer	16
rsquared	number	0.0121

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0..11)

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: `integer`

This variable doesn't seem to be used anywhere.

Parts

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

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

Use a spreadsheet or stats software to obtain the correlation coefficient $R$ between the two variables:

$R=\;$Unnamed gap

Advice

Review linear correlation and regression (e.g., Chapter 8 in OpenIntro Statistics).

Part a) and b): use Excel's CORREL function or Minitab's regression analysis.

Part c): The regression line has equation:

$\simplify[all,!collectNumbers]{y={b0}+{b1}x}$ and this is displayed below:

{regfun(r1,r2,max(r1)+10,max(r2)+10,rsquared,sumr)}

Part d):

Predicted sales when $x=\var{thisval}^{\small o}$C:

\[\begin{align} y&=\simplify[all,!collectNumbers]{{b0}+{b1}* {thisval}}\\
&=\var{{b0+b1*thisval}}\\
&=\var{prediction}
\end{align}\] in thousands of pounds.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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

Part	Test	Passed?
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Gap-fill		Hasn't run yet
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This question is used in the following exams:

Exam4SAT by Mario Orsi in Trash-backup.
Linear Regression & Correlation by Jeremie Wenger in Jeremie's workspace.
Exam May 2021 by Mario Orsi in Stats.
Sarah's copy of Exam May 2021 by Sarah Dean in Applied Scientific Practice.
ResitExam20Qs by Mario Orsi in Stats.
ResitExam by Mario Orsi in Stats.
SP test 2 by Mario Orsi in Stats.

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Linear regression and correlation - pub sales

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Linear regression and correlation - pub sales

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Mario Orsi 5 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`