Use the foilowing Inear rogression equation to answer the quesions x, \" 1.6 + 4

Question

Use the foilowing Inear rogression equation to answer the quesions x, " 1.6 + 4,0 -77Xy + 1.5 (a) Which vaable is he response vaiabe? 0 0 Which varables are the explantry variables? (Seloct al tha apply-) a b) Which number is the constant tormm? List the coeficierms win their comesponding expanatory varables cof cet , coeffciont (c) rX)-7,X5-9., and " 2. whaathe procic ed value tor x,? [Use 1 decimal place. (dl Explain how each cceticient can be hough af as a "slope" uncer certain concisons o O o ® rwe loox at all coeficients together, the sum of tem can be thought ofthe overal 'sope-ofthe regolion linlt. Ifwe look at all coeicins togather, each one can be thought of as a siope. Itwe hold al expanatory va iables as foed constants the intercept can be hought of as a slope rwe hold al other eplanaory variables asfixed oonstants, ten me oan look at one 0ffort as & sooo. Suppose and x, were hed at food but arbtrary values and K, increased by 1 unit what would be the eonesporag change ? Suppose m2 incwsed by 2 units, what would bè the expected change in x,? Suppose M2 decoased by 4 unts. what would be the xpected change in ? (o Sppose that n " 17 data pots wore used toconstruct the given Ngress ono ation and that the standard er or for the coet ciern of X is0.377. Const' ct a 90% con de o ner al fonte coff ent of x, use 2 deimal places musing the information of part e and livel of sinficance 1%, test the claim that the conciern at x2 is dferottom 2010. (Use 2decimal places.)

Explanation / Answer

a)Explanatory Variables-> x2,x3,x4

b)constant=1.8

x2 coeff=4.0

x3 coeff=-7.7

x4 coeff=1.5

c)predicted=1.8+4*7-7.7*9+1.5*2=-36.5

suppose x3,x4 were fixed,then x1 would increase by 4 units for every increase by 1 unit of x2

suppose x3,x4 were fixed,then x1 would increase by 8 units for every increase by 2 unit of x2

suppose x3,x4 were fixed,then x1 would decrease by 16 units for every decrease by 4 unit of x2

e)Lower Limit=-36.5-1.746*0.377/sqrt(16) =-37.16

Upper Limit=-36.5+1.746*0.377/sqrt(16) =-35.84

f)t critical=+-t(0.005,16)=2.921

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