Linear regression - CO2 concentration - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Stats :

Mario Orsi

said

Ready to use

5 years, 2 months ago

History

○

Mario Orsi 5 years, 2 months ago

Published this.

○

Mario Orsi 5 years, 2 months ago

Gave some feedback: Ready to use

○

Mario Orsi 5 years, 2 months ago

Saved a checkpoint:

Before renaming vars

Restore this checkpoint

○

Mario Orsi 5 years, 2 months ago

Created this as a copy of Find and use linear regression equation for a small sample.

Name	Status	Author	Last Modified
Find and use linear regression equation for a small sample	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Ed's copy of linear regression	draft	Ed Stewart	08/03/2019 05:29
Find and use linear regression equation for a small sample	draft	Xiaodan Leng	10/07/2019 22:28
Linear regression - CO2 concentration	Ready to use	Mario Orsi	19/02/2025 11:49

There are 18 other versions that do you not have access to.

Question statement

Average atmospheric levels of CO $_2$ in the 2000s (x) and 2010s (y) decades were recorded for ten locations (A-J) as reported in this table (in ppm units):

Location	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]}

Give any introductory information the student needs.

			Name	Type	Generated Value

tsqovern	list	[ 1433379.6, 1821582.4 ]
b0	number	-65.0
b1	number	1.30
obj	list	List of 10 items
r1	list	List of 10 items
r2	list	List of 10 items
ss	list	List of 2 items
res	list	List of 10 items
ssq	list	[ 1434372, 1823408 ]
n	integer	10
a	integer	18
ch	integer	5
spxy	number	1289.2
ls	number	452
tol	number	0.1
t	list	[ 3786, 4268 ]
sc	integer	398
sxy	number	1617154
b	number	1.08

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[t[0]^2/n,t[1]^2/n]

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: `list`

[ 1433379.6, 1821582.4 ]

← Depends on:

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
Part c) 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.

Use a spreadsheet or stats software to obtain the regression model $y = b_0 + b_1 \times x$:

$b_0=\;$Gap 0.ppm

$b_1=\;$Gap 1.

Advice

Part a):

Excel:

copy the table on the spreadsheet: "Ctrl-c" making sure your cursor is displayed as "I-beam" (not as pointer/arrow);
click and hold to select the data (numbers only);
click on "Insert | Charts | Scatter" to plot the data;
right-click on any data point on the plot and select "Add Trendline";
select "Display Equation on chart" to obtain the linear model.

Minitab:

copy the table on the spreadsheet, with the labels "Location (x) (y)" in the first (grey) row;
click on "Stat | Regression | Fitted Line Plot";
enter Response and Predictor as appropriate.

For part b and c, as well as generally for the underlying theory of linear correlation and regression, check your learning material (e.g., Chapter 8 in OpenIntro Statistics).

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?
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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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.
testert by cormac murphy in cormac's workspace.
CL2603StatsWeek4 by Ben Parker in Ben's workspace.
Exam May 2021 by Mario Orsi in Stats.
MA5636 Linear Regression by Ben Parker in Ben's workspace.
Sarah's copy of Exam May 2021 by Sarah Dean in Applied Scientific Practice.
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.

Loading...

Error

Linear regression - CO2 concentration

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: `list`

Parts

Gap-fill

Loading...

Error

Linear regression - CO2 concentration

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: list

Parts

Gap-fill

Generated value: `list`