Math 105 Prelim1 - Prelim 1 Solutions Problem 1(Total 10 points Give the least square line that has the best fit to the following data points(0

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Prelim 1 Solutions Problem 1 (Total 10 points) Give the least square line that has the best fit to the following data points: (0 , 2), (1 , - 2), (2 , - 2) and (3 , 2). Hint: Recall that the slope and y -intercept of the best fit line are given by the formulas nb + ± n X i =1 x i ! m = n X i =1 y i and ± n X i =1 x i ! b + ± n X i =1 x 2 i ! m = n X i =1 x i y i . Solution: We begin by computing the sums required for the equations given in the hint: n X i =1 x i = 6 n X i =1 y i = 0 n X i =1 x 2 i = 14 n X i =1 x i y i = 0 Plugging these values into the equations gives (4) b + (6) m = 0 and (6) b + (14) m = 0 Solving these equations by any method yields the unique solutions m = 0 and b = 0. Therefore the best fit line is y = 0, a horizontal line through the origin. Problem 2 (Total 16 points) Draw Venn diagrams that satisfy the following requierments. Let A U , B U , and C U and (a) ( 5 points) A B 6 = , C B and C A 6 = . (b) ( 5 points) A B 6 = and C A B. (c) ( 6 points) A B , C B 6 = , and C A 0 6 = . Solution: (Other satisfactory solutions exist. ..) 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 3 (Total 16 points) (1) Give the equations for the lines that go through the following pairs of points. Write all equations in point slope form. (a) ( 3 points) ( - 1 , 3) and (2 , 4). (b) ( 3 points) ( - 6 , - 2) and (9 , 3). (c) ( 3 points) (1 , 2) and ( - 4 , 2). (2)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/21/2008 for the course MATH 1105 taught by Professor Hurtado during the Fall '07 term at Cornell University (Engineering School).

Page1 / 5

Math 105 Prelim1 - Prelim 1 Solutions Problem 1(Total 10 points Give the least square line that has the best fit to the following data points(0

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online