What does it mean to say two quantities have negative correlation?

As one of the quantities increases, the other one decreases. The value of a car falling as the car gets older is a familiar example.

What tells you whether a correlation is strong or weak?

How close the points lie to a straight line. Points hugging a line show strong correlation, while points scattered loosely around it show weak correlation.

True or False? If two quantities are correlated, one of them must be causing the other to change.

False. Correlation does not imply causation, since both quantities may simply be changing for some third reason. A sunflower's height and a puppy's weight both rise together over one summer, but neither causes the other.

How are the points on a scatter diagram marked, and are they joined?

Each point is plotted as a cross, and the points are not joined up. What matters is the overall shape the crosses make, since that is what shows the type and the strength of the correlation.

A scatter diagram of phone time against computer time runs from top left to bottom right, with the points close to a line. Describe the correlation.

Strong negative correlation. In context that means the more time a student spends on a phone, the less time they spend on a computer.

What does zero correlation look like on a scatter diagram?

A shapeless cloud of points, with no upward or downward trend at all. It means there is no apparent relationship between the two quantities being plotted.

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

Draw one straight line with a ruler, extending across the full range of the data. There should be roughly as many points on each side along its whole length, with the gaps between the points and the line about the same on both sides.

What should you do with an outlier when drawing a line of best fit?

Ignore it. A single extreme value that does not fit the general pattern should not be allowed to pull the line away from the rest of the data.

What is the difference between interpolation and extrapolation?

Interpolation is predicting within the range of the given data, which is normally reliable. Extrapolation is predicting outside that range, which is much less reliable because there is no evidence the pattern continues.

True or False? The plotted data points on a scatter diagram will usually lie on the line of best fit.

False. The line passes between the points rather than through them, so most points sit slightly off it. That matters when finding a gradient: pick two points that are on the line , not two of the plotted data points.

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

The extra cost in pounds for each additional mile travelled. A gradient always gives the rate of change of the vertical variable with respect to the horizontal one, and it has to be read in the context of the question.

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

The fare when the distance is zero, which is the flat fee added to every ride. A y-intercept always gives the value of the vertical variable at the point where the horizontal variable equals zero.

Which point does a regression line always pass through?

The double mean point for the data set. That lets you find the mean of one variable when you know the mean of the other, by reading across from the line.

What does Spearman's rank correlation coefficient measure?

The strength of the correlation between two data sets, that is how consistently one goes up when the other goes up. It is worked out from the rankings of the values rather than from the values themselves.

Two judges rank ten jams and Spearman's coefficient comes out as −0.8. What does that tell you?

Strong negative correlation, since −0.8 is close to −1. The judges disagreed strongly: one tended to like the jams the other disliked, and the other way round.

What would a Spearman's coefficient of exactly 1 mean for two judges' rankings?

Perfect agreement: the two judges put the competitors in exactly the same order. A value of −1 would mean the two orders were exact reverses of each other, and 0 would mean no agreement either way.

True or False? A Spearman's coefficient of 1 means the points lie exactly on a straight line.

False. Spearman's coefficient only measures whether one set consistently rises as the other rises. It says nothing at all about whether the points lie along a straight line or along a curve.

What is the first thing you do when calculating a Spearman's rank correlation coefficient?

Rank the values in each of the two sets separately. You may rank from highest to lowest or from lowest to highest, but you must do the same for both sets or the answer comes out with the wrong sign.

What does a Pearson's coefficient of exactly −1 mean?

Perfect linear negative correlation. Every point lies exactly on a straight line with a negative gradient, sloping down to the right.

True or False? Pearson's coefficient and Spearman's coefficient always have the same sign as each other.

True. If the data has positive correlation both coefficients come out positive, and if it has negative correlation both come out negative. What can differ between them is how close each one gets to 1 or to −1.

Which coefficient suits data that follows a curve rather than a line?

Spearman's rank correlation coefficient, because it only asks whether one quantity consistently rises with the other. Pearson's is designed for linear correlation, so it comes out lower than Spearman's whenever the points bend away from a straight line.

If Pearson's coefficient is close to 1, what can you say about Spearman's?

It will also be close to 1. Strong linear correlation is automatically strong correlation in general, but the reverse does not follow: a high Spearman's coefficient does not guarantee a high Pearson's one.

Investment values rise with time but the points are not close to a straight line. The two coefficients are 0.9 and 0.7. Which is which?

Spearman's is 0.9 and Pearson's is 0.7. Both are positive because the trend rises, but Pearson's is held down by the points not lying close to a straight line.

GCSEStatisticsEdexcelHigherFlashcardsProcessing, Representing & Analysing DataScatter Diagrams & Correlation

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

Exam code: 1ST0

1/31

0Still learning

Know0

FrontScatter Diagrams & Correlation
Complete the sentence about scatter diagrams.
Points running from bottom left to top right show $______$ correlation, and points running from top left to bottom right show $______$ correlation.

Was this flashcard helpful?

Cards in this collection (31)

Complete the sentence about scatter diagrams.
Points running from bottom left to top right show $______$ correlation, and points running from top left to bottom right show $______$ correlation.
The completed sentence is:
Points running from bottom left to top right show positive correlation, and points running from top left to bottom right show negative correlation.
What does it mean to say two quantities have negative correlation?
As one of the quantities increases, the other one decreases.
The value of a car falling as the car gets older is a familiar example.
What tells you whether a correlation is strong or weak?
How close the points lie to a straight line.
Points hugging a line show strong correlation, while points scattered loosely around it show weak correlation.
True or False?
If two quantities are correlated, one of them must be causing the other to change.
False.
Correlation does not imply causation, since both quantities may simply be changing for some third reason.
A sunflower's height and a puppy's weight both rise together over one summer, but neither causes the other.
How are the points on a scatter diagram marked, and are they joined?
Each point is plotted as a cross, and the points are not joined up.
What matters is the overall shape the crosses make, since that is what shows the type and the strength of the correlation.
A scatter diagram of phone time against computer time runs from top left to bottom right, with the points close to a line. Describe the correlation.
Strong negative correlation.
In context that means the more time a student spends on a phone, the less time they spend on a computer.
What does zero correlation look like on a scatter diagram?
A shapeless cloud of points, with no upward or downward trend at all.
It means there is no apparent relationship between the two quantities being plotted.
What are the rules for drawing a line of best fit by eye?
Draw one straight line with a ruler, extending across the full range of the data.
There should be roughly as many points on each side along its whole length, with the gaps between the points and the line about the same on both sides.
What should you do with an outlier when drawing a line of best fit?
Ignore it.
A single extreme value that does not fit the general pattern should not be allowed to pull the line away from the rest of the data.
Define the double mean point.
The double mean point is the point whose coordinates are the mean of the $x$ values and the mean of the $y$ values, written $(\bar{x}, \bar{y})$ for a data set.
If a question mentions it, the line of best fit must be drawn through it.
What is the difference between interpolation and extrapolation?
Interpolation is predicting within the range of the given data, which is normally reliable.
Extrapolation is predicting outside that range, which is much less reliable because there is no evidence the pattern continues.
True or False?
The plotted data points on a scatter diagram will usually lie on the line of best fit.
False.
The line passes between the points rather than through them, so most points sit slightly off it.
That matters when finding a gradient: pick two points that are on the line, not two of the plotted data points.
A line of best fit plots taxi fare in pounds against distance in miles. What does its gradient mean?
The extra cost in pounds for each additional mile travelled.
A gradient always gives the rate of change of the vertical variable with respect to the horizontal one, and it has to be read in the context of the question.
A line of best fit plots taxi fare in pounds against distance in miles. What does its y-intercept mean?
The fare when the distance is zero, which is the flat fee added to every ride.
A y-intercept always gives the value of the vertical variable at the point where the horizontal variable equals zero.
What is a regression line, and how is its equation written?
A regression line is the ideal line of best fit, calculated by statistical software rather than drawn by eye, so it is more accurate than one drawn by hand.
Its equation is given in the form $y = a + b x$ for the data concerned.
A regression line has equation $y = 18.8 + 62.2 x$ where $x$ is the distance run in km. What does the 62.2 mean?
It is the gradient, so it means 62.2 more calories are burned for every extra kilometre run.
In the form $y = a + b x$ it is $b$ that gives the gradient and $a$ that gives the y-intercept.
Which point does a regression line always pass through?
The double mean point for the data set.
That lets you find the mean of one variable when you know the mean of the other, by reading across from the line.
What does Spearman's rank correlation coefficient measure?
The strength of the correlation between two data sets, that is how consistently one goes up when the other goes up.
It is worked out from the rankings of the values rather than from the values themselves.
Complete the range of possible values for Spearman's rank correlation coefficient.
$______\leq r_{S} \leq______$
The completed range is:
$- 1 \leq r_{S} \leq 1$
The closer the value lies to either end of that range, the stronger the correlation.
Two judges rank ten jams and Spearman's coefficient comes out as −0.8. What does that tell you?
Strong negative correlation, since −0.8 is close to −1.
The judges disagreed strongly: one tended to like the jams the other disliked, and the other way round.
What would a Spearman's coefficient of exactly 1 mean for two judges' rankings?
Perfect agreement: the two judges put the competitors in exactly the same order.
A value of −1 would mean the two orders were exact reverses of each other, and 0 would mean no agreement either way.
True or False?
A Spearman's coefficient of 1 means the points lie exactly on a straight line.
False.
Spearman's coefficient only measures whether one set consistently rises as the other rises.
It says nothing at all about whether the points lie along a straight line or along a curve.
What is the first thing you do when calculating a Spearman's rank correlation coefficient?
Rank the values in each of the two sets separately.
You may rank from highest to lowest or from lowest to highest, but you must do the same for both sets or the answer comes out with the wrong sign.
Ranks for six pets give differences of −3, 1, −3, 3, 3 and −1. What is $\sum d^{2}$ for this data?
Square each difference and add them: $9 + 1 + 9 + 9 + 9 + 1 = 38$ altogether.
Squaring removes the signs, so it makes no difference which ranking you subtracted from which.
With six pairs of ranks and $\sum d^{2} = 38$ , what is Spearman's rank correlation coefficient?
Substitute $n = 6$ and that sum into the formula.
$r_{S} = 1 - \frac{6 \times 38}{6 (6^{2} - 1)} = 1 - \frac{228}{210} = - 0.086$
What does Pearson's product moment correlation coefficient measure?
The strength of the linear correlation between two data sets.
It measures how close the points on a scatter diagram lie to a straight line, and it is written $r$ for a sample.
What does a Pearson's coefficient of exactly −1 mean?
Perfect linear negative correlation.
Every point lies exactly on a straight line with a negative gradient, sloping down to the right.
True or False?
Pearson's coefficient and Spearman's coefficient always have the same sign as each other.
True.
If the data has positive correlation both coefficients come out positive, and if it has negative correlation both come out negative.
What can differ between them is how close each one gets to 1 or to −1.
Which coefficient suits data that follows a curve rather than a line?
Spearman's rank correlation coefficient, because it only asks whether one quantity consistently rises with the other.
Pearson's is designed for linear correlation, so it comes out lower than Spearman's whenever the points bend away from a straight line.
If Pearson's coefficient is close to 1, what can you say about Spearman's?
It will also be close to 1.
Strong linear correlation is automatically strong correlation in general, but the reverse does not follow: a high Spearman's coefficient does not guarantee a high Pearson's one.
Investment values rise with time but the points are not close to a straight line. The two coefficients are 0.9 and 0.7. Which is which?
Spearman's is 0.9 and Pearson's is 0.7.
Both are positive because the trend rises, but Pearson's is held down by the points not lying close to a straight line.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Index Numbers & Rates of ChangeNext:Time Series