chapter 1

Chapter 12: Simple Linear Regression and Correlation29. For data set #1, r 2 = .43 and σ ˆ = s = 4. 03 ; whereas these quantities are .99 and 4.03 for #2,and .99 and 1.90 for #3. In general, one hopes for both large r 2 (large % of variationexplained) and small s (indicating that observations don’t deviate much from the estimatedline). Simple linear regression would thus seem to be most effective in the third situation.Section 12.330.2 2x i= 7,000, , so ( )( 350)V βˆ1= = .0175 and the standard7,000,000ˆβ is . 0175 = . 1323 .a. Σ( − x) 000deviation of11.0 −1.25P 1.0≤ β 1 ≤ 1.5 = P⎜≤ Z⎝ 1.323= P −1 .89 ≤ Z ≤1.89= . .1.5 −1.25≤1.323b. ( ˆ ⎛⎞) ⎟⎠( ) 94122 =1,c. Although n = 11 here and n = 7 in a, Σ( − x) 100, 000than in a. Because this appears in the denominator of V ( )the choice of x values in a.x inow, which is smallerˆβ 1, the variance is smaller for31.a. βˆ1= −. 00736023 , βˆ0=1. 41122185 , soSSE = 7 .8518 − 1.41122185 10.68 − −.00736023987.645 = . ,s 2 = .003788 , = . 06155( )( ) ( )( ) 04925s .s22ˆ =βˆ122Σxi− ( Σxi)/ n.003788= = .000001033662.25σ ,σ ˆ = s = estimated s.d. of ˆ1 = .00000103 = . 001017βˆ1βˆ1β .b. − . 00736 ± ( 2.160)( .001017) = −.00736± .00220 = ( −.00956,−.00516)366