1. 732G21/732G28/732A35 Lecture 6

2. Example second-order model with one predictor 2 Electricity consumption (Y)Home size (X) 11821290 11721350 12641470 14931600 15711710 17111840 18041980 18402230 19562400 19542930

3. Regression Analysis: Electricity cons versus X(cent), X(cent)sq The regression equation is Electricity consumption (Y) = 1703 + 0.707 X(cent) - 0.000450 X(cent)sq Predictor Coef SE Coef T P VIF Constant 1703.22 20.54 82.91 0.000 X(cent) 0.70678 0.03723 18.99 0.000 1.526 X(cent)sq -0.00045004 0.00005908 -7.62 0.000 1.526 S = 46.8013 R-Sq = 98.2% R-Sq(adj) = 97.7% Analysis of Variance Source DF SS MS F P Regression 2 831070 415535 189.71 0.000 Residual Error 7 15333 2190 Total 9 846402 Source DF Seq SS X(cent) 1 703957 X(cent)sq 1 127112  3

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5. 5 RegionSales volume Y ($10,000)TV advertising X1 ($1000)Newspaper advertising X2 ($1000) 13.2711 28.3812 311.2813 414.514 519.6315 65.8421 710.0122 812.4623 916.6724 1019.8325 118.5131 1210.1432 1314.7533 1417.9934 1519.8535 169.4641 1712.6142 1815.543 1917.6844 2021.0245 2112.2351 2213.5852 2316.7753 2420.5654 2521.0555

6. 6 RegionSales volume ($10,000) YTV advertising ($1000) X1Newspaper advertising ($1000) X2Interaction term X1X2 13.27111 28.38122 311.28133 414.5144 519.63155 65.84212 710.01224 812.46236 916.67248 1019.832510 118.51313 1210.14326 1314.75339 1417.993412 1519.853515 169.46414 1712.61428 1815.54312 1917.684416 2021.024520 2112.23515 2213.585210 2316.775315 2420.565420 2521.055525

7. Regression Analysis: Sales volume versus TV advertisi, Newspaper ad,... The regression equation is Sales volume ($10,000) = - 2.35 + 2.36 TV advertising ($1000) + 4.18 Newspaper advertising ($1000) - 0.349 Interaction term (X1X2) Predictor Coef SE Coef T P VIF Constant -2.3497 0.6883 -3.41 0.003 TV advertising ($1000) 2.3611 0.2075 11.38 0.000 5.500 Newspaper advertising ($1000) 4.1831 0.2075 20.16 0.000 5.500 Interaction term (X1X2) -0.34890 0.06257 -5.58 0.000 10.000 S = 0.625710 R-Sq = 98.6% R-Sq(adj) = 98.4% Analysis of Variance Source DF SS MS F P Regression 3 590.41 196.80 502.67 0.000 Residual Error 21 8.22 0.39 Total 24 598.63 Source DF Seq SS TV advertising ($1000) 1 86.38 Newspaper advertising ($1000) 1 491.85 Interaction term (X1X2) 1 12.17 7

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9. Salary (Y) Highschool points (X1) Art/Engineering (X2) 30 1200 27 400 35 901 44 1601 38 1601 36 1401 25 800 9

10. Regression Analysis: Salary (Y) versus Highschool p, Filfak/tekfa The regression equation is Salary (Y) = 22.5 + 0.0606 Highschool points (X1) + 7.43 Filfak/tekfak (X2) Predictor Coef SE Coef T P Constant 22.484 3.526 6.38 0.003 Highschool points (X1) 0.06062 0.03811 1.59 0.187 Filfak/tekfak (X2) 7.431 3.208 2.32 0.081 S = 3.06693 R-Sq = 85.8% R-Sq(adj) = 78.8% Analysis of Variance Source DF SS MS F P Regression 2 228.09 114.05 12.12 0.020 Residual Error 4 37.62 9.41 Total 6 265.71 Source DF Seq SS Highschool points (X1) 1 177.61 Filfak/tekfak (X2) 1 50.48 10

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