What do positive, negative and zero correlation mean?

Positive correlation means that as one quantity increases the other increases too, such as temperature and sales of cold drinks. Negative correlation means that as one quantity increases the other decreases, such as the age of a car and its value. Zero correlation means there is no apparent relationship between the two at all.

What shape do the points make for positive correlation, and for negative?

Positive correlation runs from bottom left to top right, giving a positive gradient. Negative correlation runs from top left to bottom right, while no correlation looks like a cloud of points with no direction to it.

What is the difference between strong and weak correlation on a scatter diagram?

Correlation is strong when the points lie close to a straight line. It is weak when the points are more scattered and further from lying on a line, and the strength of a correlation is a separate question from whether it is positive or negative.

A sunflower's height and a puppy's weight both increase day by day. Why does that not mean one causes the other?

Because two quantities can both be changing for a third reason, which here is simply the passing of time . Correlation shows that two things move together, but on its own it never shows that one of them causes the other.

Define association between two quantities.

Two quantities are associated when there is a relationship between them. Temperature and sales of cold drinks are associated, whereas the masses of snails and students' exam scores are not.

True or False? The points on a scatter diagram should be joined up.

False. Each pair of values is plotted as a single cross, and the crosses are left unjoined. It is the overall shape made by the scattered crosses that shows the correlation, not any line drawn between them.

A teacher finds strong negative correlation between hours spent on a phone and hours spent on a computer. What does that mean in context?

The more time a student spends on a phone, the less time that student spends on a computer. Interpreting a correlation always means turning the direction of the relationship back into a statement about the two real quantities being measured.

What are the rules for drawing a line of best fit by eye?

A line of best fit must be a straight line drawn with a ruler, extending right across the data set. There should be roughly as many points on each side of it along its whole length, with the gaps between the points and the line about the same on both sides.

When drawing a line of best fit, what do you do with an extreme value that does not fit the pattern?

Ignore it when positioning the line. A single outlier would drag the line away from the pattern that all the other points show, so the line is drawn to fit the rest of them.

What is the double mean point, and what must a line of best fit do about it?

The double mean point is the point whose coordinates are the mean of the x values and the mean of the y values. If a question mentions it then the line of best fit must be drawn through it, and if the question does not mention it there is no need to work it out at all.

Why is a prediction made outside the range of the data unreliable?

Because there is no evidence at all that the pattern carries on beyond the data that was actually collected. A line of best fit only describes the range it was drawn from, and the relationship may change or stop altogether outside that range.

A line of best fit plots taxi fare in pounds against distance travelled in miles. What does its gradient tell you?

The cost in pounds of travelling one more mile . A gradient always gives the rate of change of the y -axis quantity with respect to the x -axis quantity, and it has to be read back into the context of the question.

A line of best fit plots taxi fare in pounds against distance travelled in miles. What does its y -intercept tell you?

The fare when the distance travelled is zero , which is the flat fee added onto every taxi ride. An intercept always gives the value of the y -axis quantity at the point where the x -axis quantity is 0.

True or False? The two points used to find the gradient of a line of best fit do not have to be data points.

True. You read the coordinates of any two convenient points that lie on the line , and the plotted data points usually do not lie on it at all. Picking a plotted point that sits slightly off the line is a common way of getting the gradient wrong.

What do values of Spearman's rank close to 1, close to minus 1, and equal to 0 tell you?

Close to 1 means strong positive correlation, and close to minus 1 means strong negative correlation. A value of 0 means no correlation, and in general the closer the value sits to either 1 or minus 1, the stronger the correlation is.

Two judges rank the same competitors. What would Spearman's rank values of 1, minus 1 and 0 mean about their rankings?

A value of 1 would mean perfect agreement between the two judges. A value of minus 1 would mean their rankings were in completely opposite orders. A value of 0 would mean there was no agreement in the ranks they gave, and no consistent disagreement either.

True or False? A Spearman's rank close to 1 means the data points lie close to a straight line.

False. Spearman's rank says nothing whatever about whether the points lie along a straight line. All it measures is how consistently one quantity tends to rise when the other rises, however curved the underlying relationship might be.

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Scatter Diagrams & Correlation (Edexcel GCSE Statistics: Foundation): Flashcards

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What do positive, negative and zero correlation mean?

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What do positive, negative and zero correlation mean?
Positive correlation means that as one quantity increases the other increases too, such as temperature and sales of cold drinks.
Negative correlation means that as one quantity increases the other decreases, such as the age of a car and its value.
Zero correlation means there is no apparent relationship between the two at all.
What shape do the points make for positive correlation, and for negative?
Positive correlation runs from bottom left to top right, giving a positive gradient.
Negative correlation runs from top left to bottom right, while no correlation looks like a cloud of points with no direction to it.
What is the difference between strong and weak correlation on a scatter diagram?
Correlation is strong when the points lie close to a straight line.
It is weak when the points are more scattered and further from lying on a line, and the strength of a correlation is a separate question from whether it is positive or negative.
A sunflower's height and a puppy's weight both increase day by day. Why does that not mean one causes the other?
Because two quantities can both be changing for a third reason, which here is simply the passing of time.
Correlation shows that two things move together, but on its own it never shows that one of them causes the other.
Define association between two quantities.
Two quantities are associated when there is a relationship between them.
Temperature and sales of cold drinks are associated, whereas the masses of snails and students' exam scores are not.
True or False?
The points on a scatter diagram should be joined up.
False.
Each pair of values is plotted as a single cross, and the crosses are left unjoined.
It is the overall shape made by the scattered crosses that shows the correlation, not any line drawn between them.
A teacher finds strong negative correlation between hours spent on a phone and hours spent on a computer. What does that mean in context?
The more time a student spends on a phone, the less time that student spends on a computer.
Interpreting a correlation always means turning the direction of the relationship back into a statement about the two real quantities being measured.
What are the rules for drawing a line of best fit by eye?
A line of best fit must be a straight line drawn with a ruler, extending right across the data set.
There should be roughly as many points on each side of it along its whole length, with the gaps between the points and the line about the same on both sides.
When drawing a line of best fit, what do you do with an extreme value that does not fit the pattern?
Ignore it when positioning the line.
A single outlier would drag the line away from the pattern that all the other points show, so the line is drawn to fit the rest of them.
What is the double mean point, and what must a line of best fit do about it?
The double mean point is the point whose coordinates are the mean of the x values and the mean of the y values.
If a question mentions it then the line of best fit must be drawn through it, and if the question does not mention it there is no need to work it out at all.
Complete the two terms for making a prediction from a line of best fit.
A prediction made inside the range of the data is called $______$ , and one made outside the range of the data is called $______$ instead.
The completed terms are:
A prediction made inside the range of the data is called interpolation, and one made outside the range of the data is called extrapolation instead.
Why is a prediction made outside the range of the data unreliable?
Because there is no evidence at all that the pattern carries on beyond the data that was actually collected.
A line of best fit only describes the range it was drawn from, and the relationship may change or stop altogether outside that range.
A line of best fit plots taxi fare in pounds against distance travelled in miles. What does its gradient tell you?
The cost in pounds of travelling one more mile.
A gradient always gives the rate of change of the y-axis quantity with respect to the x-axis quantity, and it has to be read back into the context of the question.
A line of best fit plots taxi fare in pounds against distance travelled in miles. What does its y-intercept tell you?
The fare when the distance travelled is zero, which is the flat fee added onto every taxi ride.
An intercept always gives the value of the y-axis quantity at the point where the x-axis quantity is 0.
True or False?
The two points used to find the gradient of a line of best fit do not have to be data points.
True.
You read the coordinates of any two convenient points that lie on the line, and the plotted data points usually do not lie on it at all.
Picking a plotted point that sits slightly off the line is a common way of getting the gradient wrong.
What does Spearman's rank correlation coefficient measure?
The strength of the correlation between two sets of data, meaning how consistently one goes up when the other goes up, or down when the other goes up.
It is written $r_{S}$ for a sample, and it can be easier to rely on than trying to judge the strength off a scatter diagram by eye.
Complete the range of values that Spearman's rank correlation coefficient can take.
$______\leq r_{S} \leq______$
The completed range is:
$- 1 \leq r_{S} \leq 1$
A value outside that range is always a sign that something has gone wrong in the working.
What do values of Spearman's rank close to 1, close to minus 1, and equal to 0 tell you?
Close to 1 means strong positive correlation, and close to minus 1 means strong negative correlation.
A value of 0 means no correlation, and in general the closer the value sits to either 1 or minus 1, the stronger the correlation is.
Two judges rank the same competitors. What would Spearman's rank values of 1, minus 1 and 0 mean about their rankings?
A value of 1 would mean perfect agreement between the two judges.
A value of minus 1 would mean their rankings were in completely opposite orders.
A value of 0 would mean there was no agreement in the ranks they gave, and no consistent disagreement either.
Regina calculates Spearman's rank as $- 0.8$ for two judges' rankings of ten jams. What does that tell her?
The value is negative and close to minus 1, so there is strong negative correlation between the two sets of ranks.
One judge tended to like the jams that the other judge did not, so there was a great deal of disagreement between them.
True or False?
A Spearman's rank close to 1 means the data points lie close to a straight line.
False.
Spearman's rank says nothing whatever about whether the points lie along a straight line.
All it measures is how consistently one quantity tends to rise when the other rises, however curved the underlying relationship might be.

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