4B.1.1-4B.1.2 Least squares linear regression and residuals Quiz: Pearson Edexcel Further Maths, Unit 18

The 20 questions

1. What quantity does the method of least squares minimise in linear regression?

   • Sum of absolute residuals
   • Maximum vertical distance
   • Sum of squared residuals
   • Sum of horizontal errors

2. How is a residual calculated for an observed point in linear regression?

   • Observed minus mean
   • Observed minus predicted
   • Mean minus predicted
   • Predicted minus observed

3. Which point does a least squares regression line always pass through?

   • y-intercept
   • x-intercept
   • Origin
   • Mean point

4. For a least squares line with an intercept, what is the sum of the residuals?

   • Equal to RSS
   • n
   • One
   • Zero

5. What is the formula for the slope b of the least squares regression line of y on x?

   • b = Sxx / Sxy
   • b = Syy / Sxy
   • b = Sxy / Syy
   • b = Sxy / Sxx

6. Which formula calculates the residual sum of squares (RSS)?

   • Sxx - (Sxy)² / Syy
   • Syy - (Sxy)² / Sxx
   • Syy - Sxy / Sxx
   • Syy - (Sxx)² / Sxy

7. For x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 4, 5, what is the gradient of the least squares line?

   • 0.8
   • 1.2
   • 0.6
   • 0.5

8. For the same data (x = 1 to 5, y = 2, 4, 5, 4, 5), what is the intercept of the least squares line?

   • 2.0
   • 1.8
   • 2.8
   • 2.2

9. For the same data (x = 1 to 5, y = 2, 4, 5, 4, 5), what is the residual sum of squares?

   • 3.6
   • 2.4
   • 1.2
   • 6

10. For the same data (x = 1 to 5, y = 2, 4, 5, 4, 5), what is the predicted value of y at x = 6?

    • 5.8
    • 5.2
    • 6.4
    • 4.0

11. For the same data (x = 1 to 5, y = 2, 4, 5, 4, 5), what is the residual at x = 1?

    • -0.8
    • -2.8
    • 0.8
    • 2.8

12. Given Sxy = 12, Sxx = 8, x-bar = 5 and y-bar = 10, what are the slope and intercept of the least squares line?

    • b = 2.5 and a = 1.5
    • b = 1.5 and a = 2.5
    • b = 0.67 and a = 6.6
    • b = 1.5 and a = 7.5

13. Given Sxy = 20, Sxx = 16 and Syy = 50, what is the residual sum of squares?

    • 50
    • 30
    • 20
    • 25

14. Given sum of x^2 = 55, sum of x = 15 and n = 5, what is Sxx?

    • 5
    • 45
    • 10
    • 11

15. Given sum of xy = 130, sum of x = 20, sum of y = 30 and n = 5, what is Sxy?

    • 20
    • 120
    • 10
    • -10

16. A least squares line has slope b = 2, x-bar = 3 and y-bar = 7. What is the intercept?

    • 2
    • 13
    • -1
    • 1

17. What is the main purpose of examining a residual plot?

    • Determine sample size
    • Check model suitability
    • Find line gradient
    • Calculate mean y

18. How do the regression lines of y on x and x on y compare?

    • They are parallel
    • They are identical
    • They are perpendicular
    • They are different

19. What does the residual sum of squares (RSS) measure in regression?

    • Correlation coefficient
    • Explained variation
    • Total variation
    • Unexplained variation

20. Which formula is equivalent to the summary statistic Sxx?

    • Σx² - Σx / n
    • Σx² - Σx² / n
    • (Σx)² - Σx² / n
    • Σx² - (Σx)² / n

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