chapter 1

Chapter 13: Nonlinear and Multiple Regression29.a. From computer output:ŷ : 111.89 120.66 114.71 94.06 58.69y − ŷ : -1.89 2.34 4.29 -8.06 3.312 103.37SSE , s = = 51. 69, = 7. 19222Thus = ( −1.89) + ... + ( 3.31) = 103. 37s .b.( Σy)22 i2 103.37SST =Σyi− = 2630, so = 1−= . 961n2630R .H0:2= will be rejected in favor of H : β ≠ a 20 if either ≥t .= 4. 303025,2−1.84t ≤ −4.303. With t = = −3.83.480c. β 0strongly for the inclusion of the quadratic term.t or if, H o cannot be rejected; the data does not argued. To obtain joint confidence of at least 95%, we compute a 98% C.I. for each coefficientusing t 6. 965 . For β1the C.I. is 8 .06± ( 6.965)( 4.01)= ( −19.87,35.99)( an=. 01,2extremely wide interval), and for2= ( −5.18,1.50).e. t 2. 920 and ˆ + 4βˆ+ 16βˆ114. 71=. 05,2β the C.I. is − 1 .84±( 6.965)( .480)β0 1 2= , so the C.I. is 114 .71±( 2.920)( 5.01)( 100.08, 129.34)= 114 .71±14.63=.ˆˆˆf. If we knew β , β , , the value of x which maximizes0 1β2obtained by setting the derivative of this to 0 and solving:β1β ˆ ˆ +ˆ20+ β1xβ2xwould beβ1βˆ1+ 2β2x = 0 ⇒ x = − . The estimate of this is x = − = 2.19.2β2βˆ22411