5.09e Using the regression line in context Quiz: OCR Further Maths, Unit 2

The 20 questions

1. Which variable is estimated using the regression line of y on x?

   • Residual variable x
   • Independent variable x
   • Explanatory variable x
   • Response variable y

2. What term describes predicting a value outside the range of given data?

   • Regression
   • Interpolation
   • Extrapolation
   • Correlation

3. What is the main risk when using a regression line for extrapolation?

   • Zero residual error
   • Unreliable predictions
   • Negative gradient
   • Increased correlation

4. What term describes predicting a y-value within the range of observed x-values?

   • Extrapolation
   • Interpolation
   • Coding
   • Residual analysis

5. Given the regression line y = 2x + 5, what is y when x = 3?

   • 8
   • 13
   • 10
   • 11

6. If variable x is coded as u = x - 10, how does gradient change?

   • Remains unchanged
   • Increases by 10
   • Multiplied by 10
   • Decreases by 10

7. If variable y is coded as v = 2y, what happens to gradient b?

   • Increased by 2
   • Halved
   • Remains unchanged
   • Multiplied by 2

8. In the regression model y = a + bx, what does b represent?

   • y-intercept
   • Residual
   • Correlation coefficient
   • Gradient

9. In the regression model y = a + bx, what does a represent?

   • Standard deviation
   • Residual variance
   • Gradient
   • y-intercept

10. Why should a regression line of y on x NOT be used to estimate x?

    • Has zero gradient
    • Is always quadratic
    • Minimises horizontal distances
    • Minimises vertical distances

11. If coded line is v = 3u + 4 with u = x/2 and v = y, what is b?

    • 6
    • 1.5
    • 0.75
    • 3

12. What is the vertical distance between an observed point and the regression line?

    • Gradient
    • Outlier
    • Residual
    • Variance

13. If x is temperature in Celsius and y is sales, what does gradient b represent?

    • Correlation coefficient
    • Sales per degree
    • Total sales made
    • Zero degree sales

14. If x = 0 is far outside observed data, interpreting intercept a is often:

    • Statistically exact
    • Always accurate
    • Contextually invalid
    • Completely reliable

15. A regression line always passes through which point calculated from sample statistics?

    • (1, 1)
    • (s_x, s_y)
    • (0, 0)
    • (x̄, ȳ)

16. If variables x and y are coded as u = x + 5 and v = y - 3, intercept a:

    • Remains unchanged
    • Is doubled
    • Changes
    • Becomes zero

17. What does high scatter of data points around the regression line indicate?

    • High accuracy
    • High uncertainty
    • Zero residuals
    • Perfect correlation

18. To estimate x from a given y value, which regression line is required?

    • Residual line
    • Linear coding
    • y on x
    • x on y

19. What feature of data suggests a linear regression line is unsuitable?

    • Positive gradient
    • Non-linear trend
    • Non-zero intercept
    • Large sample size

20. If y = 5 + 0.4x is used to estimate y when x = 10, what is the estimate?

    • 54
    • 9
    • 5.4
    • 14

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