Explanation Given Information: The birth weights, x and lengths, y for a set of new born babies at a local hospital are given in the table as, Birth Weights and Lengths Birth Weights (in Pounds), x 5 3 8 6 9 7 7 6 6 10 Lengths (in Inches), y 16 15 18 19 19 18 20 17 15 21 Approach: The least Squares regression line is the line for which the average variation from the data is the smallest, also called the line of best fit, given by y ^ = b 0 + b 1 x . Where b 1 is the slope of the least-squares regression line for paired data from a sample and b 0 is the y -intercept for the regression line. Formula used: The equation of least-squares regression line is given by y ^ = b 0 + b 1 x Where b 1 , is the slope of the least-squares regression line, b 1 = n ∑ x i y i − ( ∑ x i ) ( ∑ y i ) n ∑ x i 2 − ( ∑ x i ) 2 and b 0 is y -intercept, b 0 = ∑ y i n − b 1 ∑ x i n Here n is the number of data pairs in the sample, x i is the i t h value of the explanatory variable and y i is the i t h value of response variable. Calculation: The table of marks scored by students in two Biology Class tests as, Birth Weights, x i Birth Lengths, y i x i y i x i 2 y i 2 5 16 80 25 256 3 15 45 9 225 8 18 144 64 324 6 19 114 36 361 9 19 171 81 361 7 18 126 49 324 7 20 140 49 400 6 17 102 36 289 6 15 90 36 225 10 21 210 100 441 ∑ x i = 67 ∑ y i = 178 ∑ x i y i = 1222 ∑ x i 2 = 485 ∑ y i 2 = 3206 In order to calculate the value of x i y i , substitute 5 for x i and 16 for y i in x i y i . x i y i = ( 5 ) ( 16 ) = 80 Proceed in the same manner to calculate x i y i for the rest of the data and refer table for the rest of the x i y i values calculated To determine (b) If the regression equation is appropriate to use for making predictions at the 0.05 level of significance and make the indicated prediction.

2nd Edition

ISBN: 9781932628678

Author: Carolyn Warren; Kimberly Denley; Emily Atchley

Publisher: Hawkes Learning Systems

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Question

Chapter 12.2, Problem 2E

To determine

(a)

To Find:

The equation of the least squares regression line.

To determine

(b)

If the regression equation is appropriate to use for making predictions at the 0.05 level of significance and make the indicated prediction.

Expert Solution & Answer

Chapter 12 Solutions

Beginning Statistics, 2nd Edition

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - Prob. 6E Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.CR - Prob. 1CR Ch. 12.CR - Prob. 2CR Ch. 12.CR - Prob. 3CR Ch. 12.CR - Prob. 4CR Ch. 12.CR - Prob. 5CR Ch. 12.CR - Prob. 6CR Ch. 12.CR - Prob. 7CR Ch. 12.CR - Prob. 8CR Ch. 12.CR - Prob. 9CR Ch. 12.CR - Prob. 10CR Ch. 12.CR - Prob. 11CR Ch. 12.CR - Prob. 12CR Ch. 12.PA - Prob. 1P Ch. 12.PB - Prob. 1P

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