Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to (A) % (B) 0% (C) 90% (D) 9% oluto The correct aswer s (D). 9% of the scaled resduals eed to be the [-,] rage to cosder a lear regresso model to be adequate. Note that ths s oe of the several cosderatos amogst others, for example, hgh coeffcet of determato, etc.
. Gve vs. x data of 0 pars are regressed to a straght le. The straght le regresso model s gve b 9 x ad the coeffcet of determato s foud to be 0.9. The correlato coeffcet s (A) 0.768 (B) 0.348 (C) 0.768 (D) 0.348 oluto The correct aswer s (A). The coeffcet of determato r s gve as 0.9, that s, r 0.9 r ±0.768 The sg of the correlato coeffcet r s determed b the slope of the regresso le. ce the slope of the regresso le 9 x s egatve, the correlato coeffcet s egatve. Hece, r 0.768
3. The followg vs. x data s regressed to a straght le. x 6 7 8 9 0.3 0.4 0.7 0.6.77 The lear regresso model s foud to be.4700 + 0. 340x. The coeffcet of determato s (A) 0.3046 (B) 0.439 (C) 0.696 (D) 0.8339 oluto The correct aswer s (C). The sum of the square of the resduals for the lear regresso model r ( a a x 0 ) ( +.4700 0.340x ) (0.3 +.4700 0.340()) + (0.4 +.4700 0.340(6)) + (0.7 +.4700 0.340(7)) + (0.6 +.4700 0.340(8)) + (.77 +.4700 0.340(9)) 0.439 + 0 a a x s gve b The sum of the squares of the dfferece betwee the depedet varable ad ts average s gve b t ( ) Now the average of the depedet varables s gve b 0.3 + 0.4 + 0.7 + 0.6 +.77 0.780
The ) ( t 0.780) ( 0.780) (.77 0.780) (0.6 0.780) (0.7 0.780) (0.4 0.780) 0.3 ( + + + +.48 Hece, the coeffcet of determato s t r t r.48 0.439.48 0.694
4. Ma tmes ou ma ot kow what regresso model to use for gve dscrete data. I such cases, a suggesto ma be to use a polomal model. But the questo remas what order of polomal to use? For example, f ou are gve 0 data pots, ou ca regress the data to a polomal order 0,,, 3, 4,, 6, 7, 8, or 9. Below s the questo ou are asked to aswer. If s the sum of the squares of the resduals ad p s the order of the polomal, the crtero ou would use to fd the optmum order of the polomal would be to fd the mmum of for all possble polomal orders. If ou have 30 data pots, the the value of m the m p formula s (A) 0 (B) 9 (C) 30 (D) 0 oluto The correct aswer s (B). The sum of the square of the resduals geerall decreases as the order of polomal s creased, ad wll fact become zero f the order of the polomal s oe less tha the umber of data pots. To fd a optmum regresso polomal order, we fd the rato of the sum of the squares of the resduals ad the dfferece betwee umber of data pots ad umber of regresso costats, that s, r Varace () ( l +) where umber of data pots, l order of polomal. Note that the umerator, that s sum of square of resduals, s zero whe f the deomator, the umber of data pots s same as the umber of regresso coeffcets (order of polomal+). The optmum order of polomal s chose whe there s a sgfcat decrease the varace as gve b equato ().
Varace 3 4 Order of Polomal, l Fgure. Varace are fucto of order of polomal. Gog back to equato () ad what s gve the questo, r r m p ( l +) Hece r ( ) l m 30 9
. O regressg data pars ( x, ),..., ( x, ) to a lear regresso model a + 0 ax, a scetst fds the regresso model to have zero slope. The regresso model the s gve b (A) (B) (C) 0 (D) x ( oluto The correct aswer s (B) ) ce for a geeral regresso model, a0 ax ad t s foud that a 0 we get a 0 0 x Hece the regresso model s gve b a + 0 ax 0x
6. Whch of the followg patters of resduals s acceptable for a lear regresso model? (A) Resduals Idepedet Varable (B) Resduals Ideoedet Varable (C) Resduals Idepedet Varable (D) Resduals Idepedet Varable oluto The correct aswer s (A). The ol acceptable patter for the resdual plots s the fgure choce (A) as t s radom. Other fgures show a patter. The fgure choce (B) ad (D) show olear behavor, whle choce (C) the fgure shows a double bow.