In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV1. (FEV1 stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s FEV1 as a function of last year’s FEV1 (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the model FEV1 = β0 + β1 Last FEV1 + β2 Gender + β3 Height + β4 Weight + β5 Height · Weight + β6 Temperature + β7 Pressure + ε a) The F statistic is?b) How many degrees of freedom does the F statistic have?c) Find the P-value for the F statistic. Is the reduced model plausible? The regression equation isFEV1 = -0.257 + 0.778 Last FEV - 0.105 Gender + 1.213 Height - 0.00624 Wei ght+ 0.00386 Height Weight - 0.00740 Temp - 0.00148 PressureSE Coef0.76020.052700.03647PredictorCoefConstant-0.25650.77818-0.10479-0.3414.77-2.872.84-0.460.7360.0000.005Last FEVGender1.2128-0.0062446HeightWeightHeight WeightTempPressure0.42700.013510.0050.6450.6470.4280.0050.00386420.0084140.0093130.46-0.007404-0.79-0.00147730.0005170-2.86S = 0.22189R-Sq = 93.5%R-Sq(adj) = 93.2%Analysis of VarianceDF7SSMS15.907F323.06SourceRegressionResidual ErrorTotal111.350.0001571647.7302119.080.049237The following MINITAB output is for a reduced model in which Weight, Height · Weight, and Temp have been dropped. Compute the Fstatistic for testing the plausibility of the reduced model.The regression equation isFEV1 = -0. 219 + 0.779 Last FEV – 0.108 Gender + 1.354 Height - 0.00134 PressurePredictorCoefSE CoefPConstantLast FEVGender-0.219470.779-0.108270.45030.049090.03520.28800.0004722-0.4915.87-3.080.6270.0000.002HeightPressure1.3536-0.00134314.70-2.840.0000.005S = 0.22039R-Sq= 93.5%R-Sq(adj)= 93.3%Analysis of VarianceSourceDFSSMSF111.31RegressionResidual Error416027.8260.048572572.890.0007.7716Total164119.08

Given Output from Minitab for fitting of model in study of children lung function with addition of…

Answered: In a study of the lung function of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 17HP

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Question

In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV₁. (FEV₁ stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s FEV₁ as a function of last year’s FEV₁ (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the model

FEV₁ = β₀ + β₁ Last FEV₁ + β₂ Gender + β₃ Height + β₄ Weight + β₅ Height · Weight + β₆ Temperature + β₇ Pressure + ε

a) The F statistic is?

b) How many degrees of freedom does the F statistic have?

c) Find the P-value for the F statistic. Is the reduced model plausible?

The regression equation is
FEV1 = -0.257 + 0.778 Last FEV - 0.105 Gender + 1.213 Height - 0.00624 Wei ght
+ 0.00386 Height Weight - 0.00740 Temp - 0.00148 Pressure
SE Coef
0.7602
0.05270
0.03647
Predictor
Coef
Constant
-0.2565
0.77818
-0.10479
-0.34
14.77
-2.87
2.84
-0.46
0.736
0.000
0.005
Last FEV
Gender
1.2128
-0.0062446
Height
Weight
Height Weight
Temp
Pressure
0.4270
0.01351
0.005
0.645
0.647
0.428
0.005
0.0038642
0.008414
0.009313
0.46
-0.007404
-0.79
-0.0014773
0.0005170
-2.86
S = 0.22189
R-Sq = 93.5%
R-Sq(adj) = 93.2%
Analysis of Variance
DF
7
SS
MS
15.907
F
323.06
Source
Regression
Residual Error
Total
111.35
0.000
157
164
7.7302
119.08
0.049237
The following MINITAB output is for a reduced model in which Weight, Height · Weight, and Temp have been dropped. Compute the F
statistic for testing the plausibility of the reduced model.
The regression equation is
FEV1 = -0. 219 + 0.779 Last FEV – 0.108 Gender + 1.354 Height - 0.00134 Pressure
Predictor
Coef
SE Coef
P
Constant
Last FEV
Gender
-0.21947
0.779
-0.10827
0.4503
0.04909
0.0352
0.2880
0.0004722
-0.49
15.87
-3.08
0.627
0.000
0.002
Height
Pressure
1.3536
-0.0013431
4.70
-2.84
0.000
0.005
S = 0.22039
R-Sq
= 93.5%
R-Sq(adj)
= 93.3%
Analysis of Variance
Source
DF
SS
MS
F
111.31
Regression
Residual Error
4
160
27.826
0.048572
572.89
0.000
7.7716
Total
164
119.08

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