Stat 501 Oct. 18 Example 1 (Data are described in first example of Chapter 7)Y = body fat, X1 = Triceps skinfold, X2 = Thigh circumference, X3 = midarm circumferenceCorrelations: Triceps, Thigh, Midarm, BodyFat Triceps Thigh MidarmThigh 0.924Midarm 0.458 0.085BodyFat 0.843 0.878 0.142Cell Contents: Pearson correlationRegression Analysis: BodyFat versus Triceps, Thigh, Midarm The regression equation isBodyFat = 117 + 4.33 Triceps - 2.86 Thigh - 2.19 MidarmPredictor Coef SE Coef T PConstant 117.08 99.78 1.17 0.258Triceps 4.334 3.016 1.44 0.170Thigh -2.857 2.582 -1.11 0.285Midarm -2.186 1.595 -1.37 0.190Source DF SS MS F PRegression 3 396.98 132.33 21.52 0.000Residual Error 16 98.40 6.15Total 19 495.39Source DF Seq SSTriceps 1 352.27Thigh 1 33.17Midarm 1 11.55Regression Analysis: BodyFat versus Midarm, Triceps, Thigh The regression equation isBodyFat = 117 - 2.19 Midarm + 4.33 Triceps - 2.86 ThighSource DF Seq SSMidarm 1 10.05Triceps 1 379.40Thigh 1 7.53Regression Analysis: BodyFat versus Thigh The regression equation isBodyFat = - 23.6 + 0.857 ThighPredictor Coef SE Coef T PConstant -23.634 5.657 -4.18 0.001Thigh 0.8565 0.1100 7.79 0.000Source DF SS MS F PRegression 1 381.97 381.97 60.62 0.000Residual Error 18 113.42 6.30Total 19 495.39Example 2 (Data described in problem 6.5)Y = rating of likeability of a pastry product, X1 = moisture content, X2 = sweetness contentCorrelations: Rating, Moisture, Sweetness Rating MoistureMoisture 0.892Sweetness 0.395 0.000Regression Analysis: Rating versus Sweetness, MoistureThe regression equation isRating = 37.7 + 4.37 Sweetness + 4.42 MoistureSource DF SS MS F PRegression 2 1872.70 936.35 129.08 0.000Residual Error 13 94.30 7.25Total 15 1967.00Source DF Seq SSSweetness 1 306.25Moisture 1 1566.45Other orderSource DF Seq SSMoisture 1 1566.45Sweetness 1 306.25One variable at a timeThe regression equation isRating = 68.6 + 4.37 SweetnessSource DF SS MS F PRegression 1 306.2 306.2 2.58 0.130Residual Error 14 1660.7 118.6Total 15 1967.0------The regression equation isRating = 50.8 + 4.42 MoistureSource DF SS MS F PRegression 1 1566.4 1566.4 54.75 0.000Residual Error 14 400.5 28.6Total 15
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