5.1. A study was conducted to ascertain the effectiveness of a treatment of diseased plants. A recorded value of Y = 1 indicates that the treatment is effective and a value of Y = 0 is recorded when no effect is noticed. The outcome of the effectiveness of the treatment considers the treatment dosage, the above ground biomass, the rate of growth and the height of a plant recorded as 1 if above average height and recorded 0 as below average height. The following partial data set is provided. EFFECTS (Y) 1 1 0 Coefficients (Intercept) HEIGHT BIOMASS The output for running the full logistic regression model is given below: RATE DOSAGE Coefficients (Intercept) BIOMASS RATE DOSAGE X₁ 0.2138 0.3907 0.2138 Log Likelihood: - 2.579 The output for the reduced model is given below: Log Likelihood: -4.246 Estimate -1.23 0.31 0.33 0.34 -1.86 BIOMASS X₂ 0.0525 0.0264 0.0920 Estimate -1.25 0.21 0.41 Std. Error 0.6795 0.6821 5.9374 2.4112 2.1420 Std. Error 0.4129 4.7390 2.4223 6 RATE X3 1.1 1.2 1.3 z value -1.653 0.456 2.594 3.167 -0866 z value -2.488 2.572 3.161 HEIGHT X4 0 1 1 Pr(>Z) 0.0984 0.6484 0.0095 0.0076 0.3864 Pr(> Z) 0.0144 0.0101 0.0076 Give the estimated logistic regression decided upon and give the odds ratios for regression coefficients b₂and b3 of this regression.
5.1. A study was conducted to ascertain the effectiveness of a treatment of diseased plants. A recorded value of Y = 1 indicates that the treatment is effective and a value of Y = 0 is recorded when no effect is noticed. The outcome of the effectiveness of the treatment considers the treatment dosage, the above ground biomass, the rate of growth and the height of a plant recorded as 1 if above average height and recorded 0 as below average height. The following partial data set is provided. EFFECTS (Y) 1 1 0 Coefficients (Intercept) HEIGHT BIOMASS The output for running the full logistic regression model is given below: RATE DOSAGE Coefficients (Intercept) BIOMASS RATE DOSAGE X₁ 0.2138 0.3907 0.2138 Log Likelihood: - 2.579 The output for the reduced model is given below: Log Likelihood: -4.246 Estimate -1.23 0.31 0.33 0.34 -1.86 BIOMASS X₂ 0.0525 0.0264 0.0920 Estimate -1.25 0.21 0.41 Std. Error 0.6795 0.6821 5.9374 2.4112 2.1420 Std. Error 0.4129 4.7390 2.4223 6 RATE X3 1.1 1.2 1.3 z value -1.653 0.456 2.594 3.167 -0866 z value -2.488 2.572 3.161 HEIGHT X4 0 1 1 Pr(>Z) 0.0984 0.6484 0.0095 0.0076 0.3864 Pr(> Z) 0.0144 0.0101 0.0076 Give the estimated logistic regression decided upon and give the odds ratios for regression coefficients b₂and b3 of this regression.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Transcribed Image Text:5.1. A study was conducted to ascertain the effectiveness of a treatment of diseased plants. A recorded
value of Y = 1 indicates that the treatment is effective and a value of Y = 0 is recorded when no
effect is noticed. The outcome of the effectiveness of the treatment considers the treatment
dosage, the above ground biomass, the rate of growth and the height of a plant recorded as 1 if
above average height and recorded 0 as below average height. The following partial data set is
provided.
EFFECTS (Y)
1
1
0
Coefficients
(Intercept)
HEIGHT
BIOMASS
RATE
DOSAGE
The output for running the full logistic regression model is given below:
Coefficients
RATE
(Intercept)
BIOMASS
DOSAGE X₁
0.2138
0.3907
0.2138
Log Likelihood: - 2.579
The output for the reduced model is given below:
Log Likelihood: -4.246
Estimate
-1.23
0.31
0.33
0.34
-1.86
BIOMASS X₂
0.0525
0.0264
0.0920
Estimate
-1.25
0.21
0.41
Std. Error
0.6795
0.6821
5.9374
2.4112
2.1420
Std. Error
0.4129
4.7390
2.4223
6
RATE X3
1.1
1.2
1.3
z value
-1.653
0.456
2.594
3.167
-0866
3.161
z value
-2.488
2.572
HEIGHT X4
0
1
1
Pr(>Z)
0.0984
0.6484
0.0095
0.0076
0.3864
Pr(>Z)
0.0144
0.0101
0.0076
Give the estimated logistic regression decided upon and give the odds ratios for regression
coefficients b₂and b3 of this regression.
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