A scatter graph plots pairs of values to show whether two variables are related. Each point is one observation.
The pattern shows correlation: positive (as one increases the other increases), negative (one increases as the other decreases), or no correlation.
For linear correlation, strength concerns how closely points follow a straight-line pattern; its steepness alone does not measure strength.
Illustrative positive association
Line of best fit
A line of best fit is a straight line drawn through the middle of the points, with roughly equal numbers of points either side. It should pass through the mean point (\bar{x}, \bar{y}).
Use it to estimate a value for one variable from the other.
Interpolation stays inside the observed x-range and is generally safer than extrapolation, but its reliability still depends on scatter, model fit and the data.
A line fitted to the illustrative data
Interpreting the line
The gradient shows the rate: how much y changes for each 1 unit of x. The intercept shows the value of y when x = 0 (not always meaningful).
Causation
Correlation does not mean causation: ice cream sales and sunburn are correlated because both rise in hot weather.
Outliers
An outlier is a point far from the pattern. Consider whether it is a mistake or genuine, and ignore it when drawing the line of best fit if it is an error.
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1.What kind of correlation do the points of a scatter graph have if they slope upwards from left to right?
Easy
Apositive
Bnegative
Cnone
Dzero
2.What kind of correlation do points have if they slope downwards from left to right?
Easy
Apositive
Bnegative
Cnone
Dperfect
3.What does 'no correlation' mean?
Easy
AThere is no clear upward or downward association in the plotted data
Bthe variables are the same
Cthe line is steep
Da strong relationship
4.What is a scatter graph used for?
Easy
Ashowing the relationship between two variables
Bshowing proportions
Cshowing frequencies in classes
Dshowing time only
5.Which would you expect to show positive correlation?
Easy
Aheight and arm span
Bage of a car and its value
Cspeed and journey time for a fixed distance
Dshoe size and number of books
6.Which would you expect to show negative correlation?
Easy
Athe age of a car and its value
Bhours of study and exam mark
Cheight and weight
Dtemperature and ice cream sales
7.For adults of a similar age, which pair would usually be expected to show no clear correlation?
Easy
Ashoe size and maths score
Bheight and weight
Ctemperature and ice cream sales
Dage of a car and value
8.A line of best fit should:
Easy
Ago through the middle of the points
Bjoin the first and last point
Cgo through the origin always
Dbe curved
もっと問題
9.Using a line of best fit to estimate a value inside the data range is called:
Easy
Ainterpolation
Bextrapolation
Ccorrelation
Dregression
10.Using a line of best fit to estimate a value outside the data range is called:
Medium
Ainterpolation
Bextrapolation
Ccorrelation
Dcausation
11.Why is extrapolation less reliable than interpolation?
Medium
Athe pattern may not continue outside the data
Bthe line is longer
Cmore data is used
Dit is always wrong
12.The line of best fit has equation y = 2x + 5 where x is hours studied and y is marks. How many marks are predicted for 10 hours?
Medium
A25
B20
C30
D15
13.A fitted line predicts exam marks y from revision hours x using y = 2x + 5. What does its gradient 2 mean?
Medium
A2 more marks per extra hour
B2 hours per mark
C5 marks per hour
D2 total marks
14.A point lies far from the rest of the data. It is called:
Medium
Aan outlier
Ba mean
Ca mode
Da median
15.Which statement is correct?
Medium
Acorrelation does not necessarily mean one variable causes the other
Bcorrelation proves causation
Cno correlation proves no link
Dall correlation is negative
16.Ice cream sales and sunburn cases are positively correlated. What is the best explanation?
Medium
Ahot weather affects both
Bice cream causes sunburn
Csunburn causes ice cream sales
Dcoincidence only
17.A scatter graph has shoe size on the x-axis and height in cm on the y-axis. Mean shoe size is 8 and mean height is 170. What is the mean point?
Medium
A(170, 8)
B(0, 0)
C(8, 170)
D(170, 170)
18.One point on a scatter graph is far from the line due to a recording error. What should you do?
Medium
ACheck the recording and correct the error, or exclude the verified erroneous point
Binclude it with extra weight
Cdelete all data
Dchange the axes
19.A scatter graph with points close to a straight line with positive gradient shows:
Medium
Astrong positive correlation
Bweak negative correlation
Cno correlation
Dstrong negative correlation
20.Which describes weak positive correlation?
Easy
Apoints scattered but loosely sloping upwards
Bpoints exactly on a line
Cpoints sloping downward
Dno pattern
21.Which variable is usually on the x-axis?
Easy
Athe independent variable
Bthe dependent variable
Ceither randomly
Dthe total
22.Hours of revision against test score gives a line y = 5x + 30. What does 30 represent?
Medium
Athe predicted score with no revision
Bthe marks per hour
Cthe maximum score
Dhours needed
23.Positive correlation means both variables increase together.
Easy
True or false?
24.Correlation proves that one variable causes the other.
Easy
True or false?
25.A line of best fit must pass through the first and last points.
Easy
True or false?
26.Extrapolation is generally less reliable than interpolation.
Easy
True or false?
27.A scatter graph with no pattern shows no correlation.
Medium
True or false?
28.Which are types of correlation?
Medium
Apositive
Bnegative
Cnone
Dcausal
Ecircular
29.For a least-squares straight-line fit with an intercept, which statements are true?
Medium
Ait goes through the middle of the points
Bit passes through the mean point
Cit can be used to estimate values
Dit must be curved
Eit must go through every point
30.What shape do the points form for strong positive correlation?
Easy
Aclose to an upward-sloping line
Bclose to a downward-sloping line
Cscattered everywhere
Da circle
31.Hours of TV watched and exam marks show negative correlation. What does that suggest?
Easy
Amore TV, lower marks on average
Bmore TV, higher marks
Cno link
DTV causes low marks
32.A scatter graph shows that as the number of hours of sunshine increases, ice cream sales increase. Describe the correlation and explain whether sunshine causes ice cream sales to increase.
