Problem #1: Given the following five pairs of(x,y) values, x 2 3 11 8 13 y 10 8

Question

Problem #1: Given the following five pairs of(x,y) values, x 2 3 11 8 13 y 10 8 5 42 (a) Determine the least squares regression line. (Be sure to save your unrounded values of Ao and A for use in Problem #2 below.) (b) Draw the least squares regression line accurately on a scatterplot. Then look to see which (x, y) pairs are above the regression line. Then add up the y-values for all of the (x,y) pairs that fall above the regression line. For example, if you draw your least squares regression line accurately on a scatterplot, and you find that the first two (x,y) pairs [i.e., (2,10) and (3,8)] are above the regression line, then since the sum of the two corresponding y-values is 10 + 8 = 18, you would enter 18 into the answer box. enter the values of 0 and 1 (in that order), separated by a comma (numbers correct to 4 decimals) sum of y-values for points above the regression line Problem #1(a): 15.588,-1.412 Problem #1(b): 15 Just Save Submit Problem #1 for Grading Problem #1 | Attempt #1 Your Answer: 1(a) 10.373, Attempt #2 | Attempt #3 1(a) 0.618 1(b) 1(a) 1(b) 1(b) 15 Your Mark: 1(a) 2/4VX 1(a) 1(b) 2/2v1(b) 1(a) 1(b Note: Your mark on each question will be the MAXIMUM of your marks on each try (So there is no harm in making another attempt at a partially correct answer.)

Explanation / Answer

Problem 1

to calculate the regression line, we require x, y , xy and x2

the table to calculate these values are

so here n = 5

and is line equation is y^ = a + bx

a= [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a = [ 29 * 367 - 37 * 157] / [5 * 367 - 372]

a = 4834/ 466 = 10.373

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b =[ 5 * 157 - 37 * 29] / [5 * 367 - 372]

b = -288/ 466 = - 0.618

so y^ = 10.373 - 0.618 x

(b) here the (2,10) and (11,5) is above the regression line.

so sum of y values = 10 + 5 = 15

Question 2

so redisuals are given in the last column.

(b) SSE =

SSE = 5.2017

(c) Test statistic : U calculated it correctly.

(d) 5% critical value for the hypothesis test.

dF = 5 -2 = 3 and alpha = 0.05

t3, 0.05 = 3.1824

(e) p - value is correct here.

x y x^2 xy 2 10 4 20 3 8 9 24 8 4 64 32 11 5 121 55 13 2 169 26 Sum 37 29 367 157

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