回歸分析實驗

習題1、考察溫度x對產量y的影響，測得下列10組數(shù)據(jù)：求y關于x的線性回歸方程，檢驗回歸效果是否顯著，并預測x=42℃溫度（℃）x20253035404550556065產量（kg）y13.215.116.417.117.918.719.621.222.524.3CoefficientsModelUnstandardizedCoefficientsStandardizedCoefficientstSig.BStd.ErrorBeta1(Constant)-39.4073.964-9.941.000x14.404.210.99120.972.000a.DependentVariable:yANOVAsModelSumofSquaresdfMeanSquareFSig.1Regression2025.65612025.656439.831.000Residual36.84484.606Total2062.5009a.Predictors:(Constant),x1b.DependentVariable:yModelSummaryModelRRSquareAdjustedRSquareStd.ErroroftheEstimate1.991.982.9802.14605因為RSquare=0.982接近于1說明方程的擬合度非常的高，并且ANOVA8表和coefficient表的sig都小于0.001所以該方程可用即：Y=4.404x-39.407所以：當x=42習題2給動物口服某種藥物A1000mg，每間隔1小時測定血藥濃度（g/ml），得到下表的數(shù)據(jù)（血藥濃度為5頭供試動物的平均值）。血藥濃度與服藥時間測定結果表：血藥濃度y(g/ml)要求：1）畫出散點圖y與x，并觀察y與x的關系；2）求y關于x的一元線性回歸方程：-----（1），求出的值；3）對上述回歸模型和回歸系數(shù)進行檢驗；4）再求y關于x的一元多項式線性回歸方程。（如：----（2）求出的值，并比較二個回歸方程對原來問題求解的優(yōu)劣。2、1）2）由線性分析可得：一元線性回歸方程為y=60.611—2.797x所以a0=60.611a1=—2.7973）ModelDescriptionModelNameMOD_2DependentVariable1x1Equation1Linear2Quadratic3Cubic4ExponentialaIndependentVariableyConstantIncludedVariableWhoseValuesLabelObservationsinPlotsUnspecifiedToleranceforEnteringTermsinEquations.0001a.Themodelrequiresallnon-missingvaluestobepositive.ModelSummaryandParameterEstimatesDependentVariable:x1EquationModelSummaryParameterEstimatesRSquareFdf1df2Sig.Constantb1b2b3Linear.097.74817.41660.611-2.797Quadratic.994481.17026.000-8.36534.827-3.762Cubic.995341.33135.000-12.82139.093-4.775.068Exponential.2091.85217.21682.026-.168Theindependentvariableisy.習題3在有氧鍛煉人中的耗氧能力y(ml(min*kg))是衡量身體狀況的重要指標，他可能與下列指標有關：年齡x1，體重x2(kg),1500m跑用的時間x3(min)，靜止時心速x4(次/min),跑步后心速x5(次/min),對24名40至57隨志愿者進行了測試，結果如下，建立耗氧能力與諸因素的回歸模型序號YX1X2X3X4X5144.64489.56.8262178245.34075.16.0462185354.34485.85.1945156459.64268.24.9040166549.93889.05.5355178644.84777.56.9858176745.74076.07.1770176849.14381.26.5164162939.44481.47.85631741060.13881.9554473.06.08451681237.44587.78.42561861344.84566.56.67511761447.24779.26.36471621551.95483.16.20501661649.24981.45.37441801740.95169.66.57571681846.85177.96.00481621950.44891.6644773.46.05671682146.15773.47.58581742246.15479.46.70621562345.45276.35.78