Lesson 5.09a-b
5.09a-b Regression lines and least squares Quiz: OCR Further Maths, Unit 2
20 questions
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Lesson 5.09a-b, Regression lines and least squares: 20 multiple choice questions for the OCR Further Maths (H245), Unit 2: Statistics (Y542), written with Revision Ninja.
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The 20 questions
-
What distance does the least squares regression line of y on x minimise?
- Absolute vertical distances
- Perpendicular distances
- Squared vertical distances
- Squared horizontal distances
-
Which point must always lie on the least squares regression line of y on x?
- Median point
- Mean point (x̄, ȳ)
- Modal point
- Origin (0, 0)
-
In linear regression analysis, how is a residual value calculated?
- Predicted minus observed
- Observed minus mean
- Observed minus predicted
- Mean minus predicted
-
In the regression line equation y = a + bx, what does b represent?
- Correlation coefficient
- Gradient
- Y-intercept
- Residual sum
-
What is the primary purpose of calculating the regression line of y on x?
- Predict x from y
- Predict y from x
- Prove causation
- Calculate correlation coefficient
-
What is predicting a dependent variable value outside the range of original data called?
- Extrapolation
- Interpolation
- Estimation
- Integration
-
What is predicting a dependent variable value inside the range of original data called?
- Expectation
- Interpolation
- Projection
- Extrapolation
-
How does the sign of the gradient b relate to the correlation coefficient r?
- Opposite sign
- Same sign
- Always positive
- No relationship
-
Given S_xy = 40 and S_xx = 10, what is the gradient b of y on x?
- 0.25
- 4
- 400
- 30
-
If mean x is 5, mean y is 12, and b is 2, what is intercept a?
- 22
- 10
- 2
- 7
-
For an observed y = 15 and predicted y = 11, what is the residual?
- 165
- -4
- 26
- 4
-
Which formula correctly calculates the summary statistic S_xy for n data pairs?
- (Σxy)^2 / n
- Σxy - ΣxΣy
- Σxy - (Σx)(Σy)/n
- Σx^2 - (Σx)^2/n
-
Which regression line minimises the sum of squared horizontal distances between points and line?
- Product moment line
- Spearman rank line
- Regression of x on y
- Regression of y on x
-
Given S_xx = 25, sum of x is 20, and n = 10, what is sum of x squared?
- 25
- 45
- 65
- 60
-
If y = 3x + 4, what is the predicted value of y when x = 5?
- 12
- 15
- 19
- 23
-
Which regression line should be used to estimate x when given a value of y?
- Line of symmetry
- Regression of x on y
- Residual line
- Regression of y on x
-
What is the formula for the residual sum of squares in regression of y on x?
- S_yy - S_xy / S_xx
- S_xy - S_xx S_yy
- S_xx - (S_xy)^2 / S_yy
- S_yy - (S_xy)^2 / S_xx
-
If x is coded as u = x - 10 and y as v = 2y, how relates gradient b to b_uv?
- b = b_uv - 10
- b = 2 b_uv
- b = b_uv / 2
- b = b_uv + 10
-
What primary effect does adding an extreme outlier have on a least squares regression line?
- Large gradient change
- Zero intercept shift
- No effect
- Perfect correlation
-
If regression gradients of y on x and x on y are 2 and 0.3, what is r^2?
- 0.6
- 0.5
- 0.15
- 6
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