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

The 20 questions

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

   • The sum of the residuals
   • The sum of the absolute values of x
   • The sum of the squared residuals
   • The product of the residuals

2. What is a residual in linear regression?

   • Predicted y plus observed y
   • Observed y minus predicted y
   • The squared difference between y and the mean of y
   • Observed x minus the mean of x

3. Where does the least squares regression line of y on x always pass?

   • The point (x-bar, 0)
   • The point (0, y-bar)
   • The origin (0, 0)
   • The point (x-bar, y-bar)

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. What is the formula for the residual sum of squares RSS?

   • RSS = Sxx - Sxy^2 / Syy
   • RSS = Syy - Sxy^2 / Sxx
   • RSS = Syy - Sxy / Sxx
   • RSS = Syy + Sxy^2 / Sxx

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. Why are residual plots examined after fitting a linear regression model?

    • To show that the residuals sum to one, so the line is correctly positioned
    • To check whether a linear model is appropriate and to spot outliers
    • To compute the slope of the regression line directly from the residual values
    • To find the mean of x, which is needed before the slope can be worked out

18. Is the regression line of y on x the same as the regression line of x on y?

    • Both lines pass through the origin
    • Yes, they always give the same line
    • They are always perpendicular
    • No, in general they give different lines

19. What does the residual sum of squares measure?

    • The slope of the fitted line, found from the covariance of x and y values
    • The mean of the residuals, which is always zero for any fitted straight line
    • The total variation of x about its mean, before any line is fitted to the data
    • The unexplained variation about the fitted line

20. Which formula gives Sxx = sum of (x - x-bar)^2?

    • sum of x^2 - sum of x
    • (sum of x)^2 - sum of x^2 / n
    • sum of x^2 + (sum of x)^2 / n
    • sum of x^2 - (sum of x)^2 / n

Related quizzes

• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions
• Definition and derivation of probability generating functions Quiz · 3B.7.1 · 20 questions