Question

Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 - 8.1X3 + 1.9x4 (a) Which variable is the response variable? O O O O Which variables are the explanatory variables? (Select all that apply.) o X3 O X4 Сх, (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient Xz coefficient x4 coefficient (C) If x2 = 8, X3 = 3, and X4 = 1, what is the predicted value for x? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. If we look at all coefficients together, each one can be thought of as a "slope." If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." Suppose x, and X4 were held at fixed but arbitrary values and x, increased by 1 unit. What would be the corresponding change in x,?

Answer 1

Solu tfon Gfven near regression equat X 1- t 3-9X1 Response Vaiable s Explanatory vaRable s constant tesm = 3.9 X2 メ3 X3=3, and X4 tS9 x2 - S1X t 9 XI S. X1-3-98) - s-1(5)+1-9 () XI10.5 hold all other eplanatory fned constant then Tf we can look vanables coeffident ac slope at one unit Xy Incea dby 3.9(X2)-8-1X3 19 xy x = 7+3-7(22 t1 )- et x341-9 xY -F3-90)81X3t9x = 1 +3-9 Y2t3-1 --1X3 t-9 Xy

E(x) 3-1 E(%) IE() E)5.G 5.G ()a t3.92 390)-8.1X31 E)J be 2un ts E C) 739E(x2)4 7.8 -81E(ya)fEy) 1.7+.8 EI) f2 decrcased by unils x be? ECX)= 39EC x2) -5.6-81Els) 7ECxy I5.G -18.9 E()= 13.9 se CB)) 0.41a to,0.085 O-05

Inceased unis 3( -2) g-111-9 1-73.9Y Confidence Interral Se (3-12 2-12 (0-4a)) (a-1e, 4.e1) aas Lower mit = .98 4-81 uppert enit 3-9 t-statistic =9.466 1 Se(A) 0.4r2 - a.6s4 tcifica o0025 aject nu hypothes, there Ps Sufficient B2 difersfrom o esfdonte that

Giren X3 8.53.72, +9.344 -2014 Ca) Response vanable Explonatorg variabe Ces Constant term 12.5 3.7 X4 -9.3 3= -18.5 3. (9) +9.3(-)--0 (9) la.5 Aold we all other Explana tory vanobles as can lock ai one coeffiuent fined con Stants, then ue slope aas

X4 ncreasec 3 units change t 9.3 (x4+3)- 2-07 ×3 ニ -8.53 E (Y3) ECX)t93E(x4)t -9-a (E(1)) 8,5 + 3 -S,5 7.9 Incrcased 1unit by X3 -18.5 f3.4 1 +9.3 t7.3 -a-017 E(15)18.53-9 E() +9.3 E) +9.3-0E) 18.5 9.3 -12 decreaced byauns X3 0ould bc -18.5 9.3(a) - 37.1 n= sa= 0-972 e) 401 confidence Interval tg,0.05 eO 86 (0.9-79) 3 t1.RG C.49 1.0) .49 Louser imit = =11-16 uppeY Rit

t stafstic -9.567 = &.306 tciHal s ts,o.0g5 tta Rijcct the nu| hypothesis there ssuffekot iifers O. from edince that Py