True or False? A scatter diagram is used to identify whether there is a relationship between two different quantities (variables).

True. A scatter diagram is used to identify whether there is a relationship between two different quantities (variables).

True or False? The data points in a strong correlation loosely follow a straight line .

False. The data points in a strong correlation closely follow a straight line . If the points only follow a straight line loosely, then they show a weak correlation.

Describe the relationship between quantity A and quantity B if they are positively correlated.

Because the quantities A and B are positively correlated , if quantity A increases , then quantity B will also increase . E.g. the number of ice creams sold by a café is positively correlated with the air temperature. As the air temperature increases, so does the number of ice creams sold by the café.

What does the phrase " correlation does not imply causation " mean?

The phrase " correlation does not imply causation " means that although a correlation may be noticed between two different quantities, it does not necessarily mean that a change in one quantity causes the other to change . E.g. the number of ice creams sold by a cafe and the number of bottles of suncream sold by a shop may be positively correlated. More ice creams being sold does not cause more bottles of sun cream to be sold, but both quantities may increase because of a third related variable, such as as an increase in the number of hours of sunshine.

Define a line of best fit .

A line of best fit is a single straight line drawn through the points on a scatter diagram to show the trend in the data. It is only worth drawing when the points show positive or negative correlation , and it can then be used to make predictions .

How should a line of best fit be drawn?

Draw a single ruled line through the mean point so that it extends across the whole data set . Tilt it until there are roughly equal numbers of points on each side along its full length.

True or False? An obvious outlier should be included when judging where to draw a line of best fit.

False. A single extreme value that does not fit the general pattern is ignored when positioning the line. Letting it drag the line away from the rest of the points would make every prediction taken from the line worse.

A line of best fit has been drawn on a scatter diagram. How do you use it to estimate y when x is 5?

Go up from 5 on the x -axis as far as the line, then across to the y -axis and read the value off there. The estimate is only trustworthy if 5 lies within the range of the original data.

Define a linear regression line .

A linear regression line is a line of best fit whose equation is calculated from the data rather than judged by eye. You obtain its equation from a graphic display calculator and are not expected to work it out by hand.

How is the data entered into a calculator to find a regression equation?

Enter it as two columns , one holding the x values and the other the y values, labelling them if the model allows it. You then tell the calculator which column is which before choosing the linear regression option.

How do you draw a regression line on a scatter diagram from its equation?

Choose any two x values, substitute each into the equation to find its y value, and plot the two points. Join them with a ruled straight line ; the two x values do not have to match any of the data points.

True or False? A regression line and a line of best fit drawn by eye will always come out identical.

False. A line drawn by eye is a judgement, so two people can draw different ones through the same set of points. The regression line is calculated from the data, which is why it is treated as the more accurate of the two.

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Scatter Graphs & Correlation (Cambridge (CIE) IGCSE International Maths: Extended): Flashcards

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FrontScatter Graphs & Correlation
True or False?
A scatter diagram is used to identify whether there is a relationship between two different quantities (variables).

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Cards in this collection (20)

True or False?
A scatter diagram is used to identify whether there is a relationship between two different quantities (variables).
True.
A scatter diagram is used to identify whether there is a relationship between two different quantities (variables).
What type of correlation is shown in the diagram below?
The type of correlation shown is negative correlation.
The data points follow a general trend from the top left of the graph to the bottom right.
True or False?
The data points in a strong correlation loosely follow a straight line.
False.
The data points in a strong correlation closely follow a straight line.
If the points only follow a straight line loosely, then they show a weak correlation.
Describe the relationship between quantity A and quantity B if they are positively correlated.
Because the quantities A and B are positively correlated, if quantity A increases, then quantity B will also increase.
E.g. the number of ice creams sold by a café is positively correlated with the air temperature. As the air temperature increases, so does the number of ice creams sold by the café.
What does the phrase "correlation does not imply causation" mean?
The phrase "correlation does not imply causation" means that although a correlation may be noticed between two different quantities, it does not necessarily mean that a change in one quantity causes the other to change.
E.g. the number of ice creams sold by a cafe and the number of bottles of suncream sold by a shop may be positively correlated.
More ice creams being sold does not cause more bottles of sun cream to be sold, but both quantities may increase because of a third related variable, such as as an increase in the number of hours of sunshine.
Define a line of best fit.
A line of best fit is a single straight line drawn through the points on a scatter diagram to show the trend in the data.
It is only worth drawing when the points show positive or negative correlation, and it can then be used to make predictions.
How do you find the mean point of a set of data on a scatter diagram?
Work out the mean of all the x values to get $\bar{x}$ and the mean of all the y values to get $\bar{y}$ separately.
The mean point is then $(\bar{x}, \bar{y})$ plotted on the diagram alongside the data.
How should a line of best fit be drawn?
Draw a single ruled line through the mean point so that it extends across the whole data set.
Tilt it until there are roughly equal numbers of points on each side along its full length.
Complete the two terms for making predictions from a line of best fit.
Predicting inside the region covered by the data is called $______$ and is reliable, while predicting well outside it is called $______$ and is much less so.
The completed sentence is:
Predicting inside the region covered by the data is called interpolation and is reliable, while predicting well outside it is called extrapolation and is much less so.
An extrapolated value assumes the trend carries on beyond the data, which the data itself gives no evidence for.
True or False?
An obvious outlier should be included when judging where to draw a line of best fit.
False.
A single extreme value that does not fit the general pattern is ignored when positioning the line.
Letting it drag the line away from the rest of the points would make every prediction taken from the line worse.
A line of best fit has been drawn on a scatter diagram. How do you use it to estimate y when x is 5?
Go up from 5 on the x-axis as far as the line, then across to the y-axis and read the value off there.
The estimate is only trustworthy if 5 lies within the range of the original data.
Eight computers have prices with a mean of 487.5 and running times with a mean of 3.9. Which point must the line of best fit pass through?
The line must pass through the mean point, which is $(487.5, 3.9)$ for this data.
Every line of best fit drawn for this data set has to go through that one point, whatever gradient it ends up with.
Define a linear regression line.
A linear regression line is a line of best fit whose equation is calculated from the data rather than judged by eye.
You obtain its equation from a graphic display calculator and are not expected to work it out by hand.
In the regression equation $y = m x + b$ what do m and b stand for?
m is the gradient of the line and b is its y-intercept.
It is the same straight line equation as $y = m x + c$ with the letter b used in place of c here.
How is the data entered into a calculator to find a regression equation?
Enter it as two columns, one holding the x values and the other the y values, labelling them if the model allows it.
You then tell the calculator which column is which before choosing the linear regression option.
Complete the rule for writing down a regression equation.
Round the values of m and b to $______$ significant figures each, unless they can be written exactly.
The completed rule is:
Round the values of m and b to 3 significant figures each, unless they can be written exactly.
Substituting the rounded values back into $y = m x + b$ gives the equation you write down.
True or False?
A regression line passes exactly through the mean point of its data set.
True.
A line drawn from the regression equation always goes through $(\bar{x}, \bar{y})$ exactly, not just close to it.
That makes it a useful check, and it lets you work out a missing mean from the equation.
The regression line for a data set is $y = 62.1 x + 20.0$ and the mean of the x values is 8. What is the mean of the y values?
Substitute $x = 8$ into the equation, since the mean point lies on the line.
That gives $62.1 \times 8 + 20.0 = 516.8$ so the mean of the y values is about 517.
How do you draw a regression line on a scatter diagram from its equation?
Choose any two x values, substitute each into the equation to find its y value, and plot the two points.
Join them with a ruled straight line; the two x values do not have to match any of the data points.
True or False?
A regression line and a line of best fit drawn by eye will always come out identical.
False.
A line drawn by eye is a judgement, so two people can draw different ones through the same set of points.
The regression line is calculated from the data, which is why it is treated as the more accurate of the two.

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