regression_solution.pdf

# 1 4 1 8 mtb tran m1 m2 mtb print m2 53 data display

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?×? 1 -4 1 -8 MTB > tran m1 m2 MTB > print m2 ?′ ?×?

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53 Data Display Matrix M2 1 1 1 1 1 8 4 0 -4 -8 ?′ ?×? MTB > mult m2 m1 m3 MTB > print m3 (?′?) ?×? Data Display Matrix M3 (?′?) ?×? = [ ? ∑ ? 𝑖 ∑ ? 𝑖 ∑ ? 𝑖 2 ] 5 0 0 160 MTB > inver m3 m4 MTB > print m4 (?′?) ?×? −? Data Display Matrix M4 0.2 0.00000 0.0 0.00625 MTB > copy c2 m5 MTB > Print m5 ? ?×?
54 Data Display Matrix M5 7.8 9.0 ? ?×? 10.2 11.0 11.7 MTB > mult m2 m5 m6 MTB > print m6 ?′ ?×? ? ?×? = ?′? ?×? Data Display Matrix M6 49.7 -39.2 MTB > mult m4 m6 m7 MTB > print m7 (?′?) ?×? −? (?′?) ?×? = 𝚩 ?×? Data Display Matrix M7 9.940 𝚩 ?×? -0.245 ? ̂ = 9.940 − 0.245?

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55 MTB > tran m5 m13 MTB > print m13 Data Display Matrix M13 7.8 9 10.2 11 11.7 MTB > mult m13 m5 m14 Answer = 503.7700 MTB > mult m1 m7 m8 ? ̂ ?×? = ? ?×? 𝚩 ?×? MTB > print m8 Data Display Matrix M8 7.98 8.96 9.94 10.92 11.90 MTB > copy m8 c4
56 MTB > Let c5 = 'y'-C4 MTB > copy c5 m9 𝒆 MTB > tran m9 m10 MTB > print m10 𝒆′ Data Display Matrix M10 -0.18 0.04 0.26 0.08 -0.2 MTB > mult m10 m9 m11 𝒆′𝒆 Answer = 0.1480 MSE=0.1480/3=0.049333 𝑴?𝑬 = 𝒆′𝒆 ?−? MTB > mult 0.049333 m4 m12 MTB > print m12 𝑽(𝚩) = 𝑴?𝑬(?′?) −? Data Display Matrix M12 0.0098666 0.0000000 0.0000000 0.0003083

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57 𝑽 [ ? 0 ̂ ? 1 ̂ ] = [ 𝑽?𝒓(? 0 ̂ ) ??𝒗(? 0 ̂ , ? 1 ̂ ) ??𝒗(? 0 ̂ , ? 1 ̂ ) 𝑽?𝒓(? 1 ̂ ) ] Regression Analysis: y versus x Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 9.6040 9.60400 194.68 0.001 x 1 9.6040 9.60400 194.68 0.001 Error 3 0.1480 0.04933 Total 4 9.7520 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.222111 98.48% 97.98% 94.11% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 9.9400 0.0993 100.07 0.000 x -0.2450 0.0176 -13.95 0.001 1.00 Regression Equation y = 9.9400 - 0.2450 x
58 H.W Q5.2 For the matrices below, obtain (1) ? + ? , (2) ? − ? , (3) ?′ ? , (4) ??′ , (5) ?′ ? . ? = [ 2 1 3 5 5 4 7 8 ] ? = [ 6 9 3 1 ] ? = [ 3 8 8 6 5 2 1 4 ] Q5.5 Consumer finance. The data below show, for a consumer finance company operating in six cities, the number of competing loan companies operating in the city (X) and the number per thousand of the company's loans made in that city that are currently delinquent (Y); i 1 2 3 4 5 6 ? 𝑖 4 1 2 3 3 4 ? 𝑖 16 5 10 15 13 22 Assume that first-order regression model (2.1) is applicable. Using matrix methods, find (1) ?′?, (2) ?′?, (3) ?′? .
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• Spring '18
• Dr Ribble

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