~v200 200 ~w38 0 442 624 1408 1393 0 0 ~f? 14 12 10 ? 0 0 0 1 ? ? ? "Times New Roman" ? ? ? 1 ? 0 1 "Times" 12 ? ? 5 0 c n 112 1 0 0 k 396 f"?n page ?p?a" -2 0 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 0 0 -1 -1 -1 -1 -1 1 1 ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b&*" *^: ;bP8&c0!* `f#};bP;Multiple| | Regression with Least Squares}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?v0 (yfit)~p0 1 ~V?v0 (xthree)~p0 1 ~V?v0 (xtwo)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *^: ;bP8&c0!*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(Lower=yf-t'a*StdErrOfForecast)~p0 2 ~A(Upper=yf+t'a*StdErrOfForecast)~p0 2 ~A(StdErrOfForecast=ErrorVar(x,y)*sqrt(1+1/(RowsOf(x))+xf*(x^**~ x)^(-1)*xf^*))~p0 2 ~d~A(StdErrOfForecast=12.344220363371099)~p0 3 ~sb/_! ! } $& ! c#T"!c"H"_c/__c/__} ^ _~A(yf=xf*Beta(x,y))~p0 2 ~d~A(F(H,h,x,y))~p0 2 ~A(StudentT(R,r,x,y))~p0 2 ~A(Rsq(x,y))~p0 2 ~A(ErrorVar(x,y))~p0 2 ~A(CoeffCov(x,y))~p0 2 ~A(Beta(x,y))~p0 2 ~V?v0 (Upper)~p0 2 ~V?v0 (Lower)~p0 2 ~V?v0 (t'a)~p0 2 ~V?v0 (yf)~p0 2 ~V?v0 (StdErrOfForecast)~p0 2 ~V?v0 (xf)~p0 2 ~V?v0 (Yf)~p0 2 ~V?m0 (h)~p0 2 ~V?m0 (H)~p0 2 ~V?f0 (F)~p0 2 ~V?v0 (r)~p0 2 ~V?m0 (R)~p0 2 ~V?f0 (StudentT)~p0 2 ~V?v0 (j)~p0 2 ~V?f0 (Mean)~p0 2 ~V?f0 (TSS)~p0 2 ~V?f0 (Rsq)~p0 2 ~V?f0 (ErrorVar)~p0 2 ~V?f146 (ColumnsOf)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f0 (CoeffCov)~p0 2 ~V?f0 (RSS)~p0 2 ~V?f0 (Beta)~p0 2 ~V?c3 ('N)~p0 2 ~V?f0 ('F)~p0 2 ~V?f0 (f)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?c1 ('p)~p0 3 ~V?f256 (sin)~p0 3 ~V?f257 (cos)~p0 3 ~V?f258 (tan)~p0 3 ~V?f261 (sec)~p0 3 ~V?f260 (csc)~p0 3 ~V?f262 (cot)~p0 3 ~V?f272 (arcsin)~p0 3 ~V?f273 (arccos)~p0 3 ~V?f274 (arctan)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f293 (sech)~p0 3 ~V?f288 (sinh)~p0 3 ~V?f289 (cosh)~p0 3 ~V?f290 (tanh)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *^: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f32 (log)~p0 3 ~V?f307 (ln)~p0 3 ~V?f291 (exp)~p0 3 ~V?c2 (e)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *^: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(?x^(-?y)):(1/?x^?y)~p0 4 ~Hs(exp(?z)):(e^?z)~p0 4 ~Hs(e^(ln(?x))):(?x)~p0 4 ~Hs(10^(log(?x))):(?x)~p0 4 ~Hs(?y^(log_?y(?x))):(?x)~p0 4 ~Hs(ln(e^?x)):(?x)~p0 4 ~Hs(log(10^?x)):(?x)~p0 4 ~Hs(log_?y(?y^?x)):(?x)~p0 4 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 4 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 4 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 4 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 4 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 4 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 4 ~He(ln(?u^?v)):(?v*ln(?u))~p0 4 ~He(log(?u^?v)):(?v*log(?u))~p0 4 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 4 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 4 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 4 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *^: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *^: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Hs(sin(-?x)):(-sin(?x))~p0 5 ~Hs(cos(-?x)):(cos(?x))~p0 5 ~Hs(tan(-?x)):(-tan(?x))~p0 5 ~Hs(sin('p)):(0)~p0 5 ~Hs(sin(?n*'p)):(0)~p0 5 ~Hs(cos(1/2*'p)):(0)~p0 5 ~Hs(cos(?n/2*'p)):(0)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *^: ;bP8&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 5 ~Ht(csc(?x)):(1/(sin(?x)))~p0 5 ~Ht(sin(?x)):(1/(csc(?x)))~p0 5 ~Ht(sec(?x)):(1/(cos(?x)))~p0 5 ~Ht(cos(?x)):(1/(sec(?x)))~p0 5 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 5 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 5 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 5 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 5 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*sin((?n-1)*?x))~p0 5 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*sin((?n-1)*?x))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" *^: ;bP8&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 5 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 5 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 5 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 5 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 5 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 5 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *^: ;bP8&c0!*substituting | |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 5 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 5 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 5 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 5 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 5 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" *^: ;bP8&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *^: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Hs(sinh(-?x)):(-sinh(?x))~p0 5 ~Hs(cosh(-?x)):(cosh(?x))~p0 5 ~Hs(tanh(-?x)):(-tanh(?x))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *^: ;bP8&c0!*Transform into | |other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0 5 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0 5 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0 5 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0 5 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0 5 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0 5 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0 5 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0 5 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *^: ;bP8&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 5 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 5 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 5 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *^: ;bP8&c0!*Integration Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b$8" *^: ;bP8&c0!*after Partial Fraction| | Decomposition integration}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 4 ~Hs(ln(?x+?b*i)):((-i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~ i)~p0 5 ~Hs(ln(?x+i)):((-i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0 5 ~Hs(ln(?x-?b*i)):((i*arctan(?x/?b)+1/2*ln(?x^2+?b^2))+1/2*'p*~ i)~p0 5 ~Hs(ln(?x-i)):((i*arctan(?x)+1/2*ln(?x^2+1))+1/2*'p*i)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$4" *^: ;bP8&c0!*Derivatives of | |Integrals}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 4 ~Ht(Diff(?x)*(Integral(?y*d*?x))):(?y)~p0 5 ~V?c4 (i)~p0 2 ~V?d16 (d)~p0 2 ~V?v0 (k)~p0 2 ~V?c0 (n)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?v0 (z)~p0 2 ~V?m0 (y)~p0 2 ~V?m0 (x)~p0 2 ~A(StudentT(?r,?g,?x,?y)=(?r*Beta(?x,?y)-?g)/(ErrorVar(?x,?y)*~ ?r*(?x^**?x)^(-1)*?r^*)^(1/2))~p0 2 ~d~A('F(?x)=1/sqrt(2*'p)*(Integral(e^(-y^2/2)*d*y):(-'N):(?x)))~p0 2 ~d~A('F(2))~p0 2 ~A('F(2)=0.97724986796407132)~p0 3 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(Beta(?x,?y)=(?x^**~ ?x)^(-1)*?x^**?y)~p0 2 ~d~A(RSS(?x,?y)=(?y-?x*Beta(?x,?y))^**(?y-?x*Beta(?x,?y)))~p0 2 ~d~A(TSS(?x,?y)=Summation(j):(1):(RowsOf(?y))*(y_j-Mean(?y))^~ 2)~p0 2 ~d~A(Mean(?y)=1/(RowsOf(?y))*Summation(j):(1):(RowsOf(?y))*?y_~ j)~p0 2 ~d~A(ErrorVar(?x,?y)=(RSS(?x,?y))/(RowsOf(?x)-ColumnsOf(?x)))~p0 2 ~d~A(CoeffCov(?x,?y)=ErrorVar(?x,?y)*(?x^**?x)^(-1))~p0 2 ~d~A(Rsq(?x,?y)=1-(RSS(?x,?y))/(TSS(?x,?y)))~p0 2 ~d~A(F(?r,?g,?x,?y)=(((?r*Beta(?x,?y)-?g)^**(?r*(?x^**?x)^(-1)*~ ?r^*)^(-1)*(?r*Beta(?x,?y)-?g))/(RowsOf(?r)))/(ErrorVar(?x,?y)))~p0 2 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&*}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})b!># b&,`fb#@}" *^: ;bP8&c0!*Problem| |,Z`f } We are given the model y ,]"!Symbol^:!&c0 : &c0!*x:!&c0 b| |: &c0!* ,K u, ,L in which the coefficients,L :!&c0 b: &c0!*,L| | are k parameters that are unknown to us,N The error term is| | assumed to be N,H:!&c0 m: &c0!*,L, $^:!&c0 s_^: &c0!*2,I,N| | From the data we must estimate the unknowns,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})b!=# b&," *^: ;bP8&c0!*Enter your data| | here,N If you want to add a column put your cursor on the last| | element in the first row and type ,B,L,B,N To append a row | |put the cursor on the last element in the last row and type ,B| |,[,B,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})"# b&," *^: ;bP8&c0!* | |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(x=(1,2,-1;1,6,2;1,9,9;1,13,5;1,17,3;1,19,1;1,21,-2))~p0 0 ~d~A(y=(1;7;17;12;13;14;19))~p0 255 ~d~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})## b&," *^: ;bP8&c0!*Coefficient| | Estimates}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})1# b&," *^: ;bP8&c0!*For your data the| | least squares coefficient estimates are| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Beta(x,y)=(0.69982572570281043;0.75744186455894569;0.71786927667364919))~p0 0 ~sb/^!! } $&! c#T"!c#L"_c/__c/__} ^ _~Z1 1 273 273 0 0.89969 -0.43654 0.00000 -0.32693 -0.67379 -0.66266 0.28927 0.59619 -0.74891 1 5 6 3 10 0 0 ? ? (~ -2...25):(-2...10):(-2...25):(?=0...2*'p):('p/5):(10)~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#@" *^: ;bP8&c0!*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~X2 8405120 (west,south,y):(y=bottom...top):(y)~p0 1 ~gc1 6 ? 0 -4096 -4096 -4096 14745 -4096 -4096 -2253 26214 -4096 -4096 -819 39321 -4096 -4096 819 50790 -4096 -4096 2253 65535 -4096 -4096 4096 ~ ~X2 8405120 (west,xthree,bottom):(xthree=south...north):(xthree)~p0 1 ~gc1 6 ? 0 -4096 -4096 -4096 14745 -4096 -2253 -4096 26214 -4096 -819 -4096 39321 -4096 819 -4096 50790 -4096 2253 -4096 65535 -4096 4096 -4096 ~ ~X1 8405120 (xtwo,south,bottom):(xtwo=west...east):(xtwo)~p0 1 ~gc1 6 ? 0 -4096 -4096 -4096 14745 -2253 -4096 -4096 26214 -819 -4096 -4096 39321 819 -4096 -4096 50790 2253 -4096 -4096 65535 4096 -4096 -4096 ~ ~V?c69 (west)~p0 1 ~V?c68 (east)~p0 1 ~V?c70 (south)~p0 1 ~V?c71 (north)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~S17 ? 255 ? ? (x_(j,2),x_(j,3),y_j):(j=1...RowsOf(x)):(8)~p0 0 ~gc-1 7 ? 0 -2882 -3413 -3186 12287 -1669 -1365 -1365 21845 -759 3413 1669 32767 455 683 152 42325 1669 -683 455 55977 2276 -2048 759 65535 2882 -4096 2276 ~ ~D2 5 1 16777215 ? ? (xtwo,xthree,yfit):(xtwo=west...east):(xthree=~ south...north):(yfit=bottom...top)~p0 0 ~gs9 9 0 0 ? -1056964609 -4096 -4096 -4172 -1056964609 -4096 -3072 -3845 -1056964609 -4096 -2048 -3519 -1056964609 -4096 -1024 -3192 -1056964609 -4096 0 -2865 -1056964609 -4096 1024 -2538 -1056964609 -4096 2048 -2212 -1056964609 -4096 3072 -1885 -2147483648 -4096 4096 -1558 -1056964609 -3072 -4096 -3396 -1056964609 -3072 -3072 -3070 -1056964609 -3072 -2048 -2743 -1056964609 -3072 -1024 -2416 -1056964609 -3072 0 -2090 -1056964609 -3072 1024 -1763 -1056964609 -3072 2048 -1436 -1056964609 -3072 3072 -1109 -2147483648 -3072 4096 -783 -1056964609 -2048 -4096 -2621 -1056964609 -2048 -3072 -2294 -1056964609 -2048 -2048 -1967 -1056964609 -2048 -1024 -1641 -1056964609 -2048 0 -1314 -1056964609 -2048 1024 -987 -1056964609 -2048 2048 -660 -1056964609 -2048 3072 -334 -2147483648 -2048 4096 -7 -1056964609 -1024 -4096 -1845 -1056964609 -1024 -3072 -1518 -1056964609 -1024 -2048 -1192 -1056964609 -1024 -1024 -865 -1056964609 -1024 0 -538 -1056964609 -1024 1024 -212 -1056964609 -1024 2048 115 -1056964609 -1024 3072 442 -2147483648 -1024 4096 769 -1056964609 0 -4096 -1070 -1056964609 0 -3072 -743 -1056964609 0 -2048 -416 -1056964609 0 -1024 -89 -1056964609 0 0 237 -1056964609 0 1024 564 -1056964609 0 2048 891 -1056964609 0 3072 1217 -2147483648 0 4096 1544 -1056964609 1024 -4096 -294 -1056964609 1024 -3072 33 -1056964609 1024 -2048 360 -1056964609 1024 -1024 686 -1056964609 1024 0 1013 -1056964609 1024 1024 1340 -1056964609 1024 2048 1666 -1056964609 1024 3072 1993 -2147483648 1024 4096 2320 -1056964609 2048 -4096 482 -1056964609 2048 -3072 808 -1056964609 2048 -2048 1135 -1056964609 2048 -1024 1462 -1056964609 2048 0 1789 -1056964609 2048 1024 2115 -1056964609 2048 2048 2442 -1056964609 2048 3072 2769 -2147483648 2048 4096 3095 -1056964609 3072 -4096 1257 -1056964609 3072 -3072 1584 -1056964609 3072 -2048 1911 -1056964609 3072 -1024 2237 -1056964609 3072 0 2564 -1056964609 3072 1024 2891 -1056964609 3072 2048 3218 -1056964609 3072 3072 3544 -2147483648 3072 4096 3871 -2147483648 4096 -4096 2033 -2147483648 4096 -3072 2360 -2147483648 4096 -2048 2686 -2147483648 4096 -1024 3013 -2147483648 4096 0 3340 -2147483648 4096 1024 3667 -2147483648 4096 2048 3993 -2147483648 4096 3072 4320 -2147483648 4096 4096 4647 ~t~p1 0 ~A(yfit=(Beta(x,y))_1+(Beta(x,y))_2*xtwo+(Beta(x,y))_3*xthree)~p0 1 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})b H# b%>" *^: ;bP8&c0!*The blue dots| | are a scattergram of the data,N The plane is a graph of the| | sample regression function,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#}))# b&," *^: ;bP8&c0!*Estimate | |of the Error Variance}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})-# b&," *^: ;bP8&c0!*For your data the| | error variance is}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(ErrorVar(x,y)=9.8593747249458676)~p0 0 ~sb/^! ! } $& ! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})+# b&," *^: ;bP8&c0!*Estimate | |of the Coefficient Covariance Matrix}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b&," *^: ;bP8&c0!*For your data the| | coefficient covariance matrix is}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(CoeffCov(x,y)=(0.53466980361402527,-0.067395353396725907,0.022465117798908644;~ -0.067395353396725879,0.014908669084730274,-0.01184524393033364;~ 0.02246511779890863,-0.01184524393033364,0.017699789780958309))~p0 0 ~sb/^! ! } $& ! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})%# b&," *^: ;bP8&c0!*Goodness | |of Fit}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})9# b%L" *^: ;bP8&c0!*For your data the| | coefficient of determination,L or goodness of fit,L is| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Rsq(x,y)=0.82461086893361868)~p0 0 ~sb/^! ! } $& ! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_}) # b&,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})## b&," *^: ;bP8&c0!*Hypothesis| | Testing}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#C})*# b&," *^: ;bP8&c0!* The Student| | t ,M test}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})b"+# b&," *^: ;bP8&c0!*We will do a | |general form of the Student t ,M test,N The null and alternate| | hypotheses are of the sort $^H^0_,Z R"!Symbol^:!&c0 b: &c0!* | |,M r ,] 0 versus $^H^1_,ZR:!&c0 b: &c0!* ,M r `g| |Mb.3b+<| |!!!!)!!!%\!!!%t!!!!!!!rW+!G2E6!!`K(!!!!6!#,D5"ss!\jZT!!!!"!!!!&| |!It4[!"o<_"ss!A+9O!!E9*| |!Up'h!!`K,!rN#us8N'!!!!$!!!!!%!!E[!!!!%!!!$O| |!!!!%!!**%!!!!&!!!',!!<3$!$2+?!!!!(!&=Zm!!!!P!"],1"ssPF| |s8W-!s8N'!s8W-!!&OZT!&FTT!!<3$!$2+?!!!!%!!!$P!!!!&!!!'-!!N?&| |!XSi,!!!!!!!!!&s8N-$!!`N(!rN#u!!!!"!!!!!!!!!%!!**P!!!!*!!NH#| |!!!!!!<<*!!!E9G!A+9O!!E9'!# b&," *^: ;bP8&c0!*Choose an appropriate| | t statistic for the necessary degrees of freedom and level of| | confidence,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(t'a=2.1320000000000001)~p0 0 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})b G# b&," *^: ;bP8&c0!*For you realization| | of x and level of confidence,L the upper and lower bounds on| | the prediction interval are,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(Lower=-9.9887810484635899)~p0 0 ~sb/_! ! } $& ! c#T"!c"L"_c/__c/__} ^ _~A(Upper=42.646974580950783)~p0 0 ~sb/_! ! } $& ! c#T"!c"L"_c/__c/__} ^ _~c13 8 -1 7 -1 217 -1 21 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 168 -1 37 -1 171 -1 33 -1 ~c3 166 -1 165 -1 164 -1 40 -1 ~c7 185 -1 15 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 ~c11 192 -1 13 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 168 -1 37 -1 171 -1 33 -1 ~c9 196 -1 14 -1 167 -1 38 -1 168 -1 37 -1 171 -1 33 -1 172 -1 36 -1 ~c15 200 -1 12 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 168 -1 37 -1 170 -1 30 -1 169 -1 31 -1 173 -1 32 -1 ~c17 207 -1 11 -1 205 -1 27 -1 206 -1 26 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 168 -1 37 -1 171 -1 33 -1 163 -1 28 -1 ~c17 213 -1 10 -1 211 -1 24 -1 212 -1 23 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 168 -1 37 -1 171 -1 33 -1 174 -1 25 -1 ~c9 218 -1 9 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 217 -1 21 -1 ~c19 222 -1 5 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 217 -1 21 -1 9 -1 19 -1 168 -1 37 -1 171 -1 33 -1 7 -1 20 -1 220 -1 18 -1 ~c19 223 -1 6 -1 180 -1 162 -1 181 -1 161 -1 167 -1 38 -1 217 -1 21 -1 9 -1 19 -1 168 -1 37 -1 171 -1 33 -1 7 -1 20 -1 220 -1 18 -1 ~e