a) What are the estimated intercept and estimated slope for the regression of lo
ID: 3244781 • Letter: A
Question
a) What are the estimated intercept and estimated slope for the regression of log energy on log mass for i) non-echo locating bats, ii) non-echo locating birds, and iii) echo locating bats?
b) Refit the model using the indicator variables bird and nbat, where nbat takes on the value 1 for species of non-echo locating bats and 0 for other species
c) What are the estimated intercept and estimated slope for the regression of log energy on log mass for three species?
d) Test whether the lines for echo locating bats and non-echo locating birds coincide
Data Display
Row Mass Type Energy LN(Energy) LN(Mass) ebat nebat bird
1 779.0 non-echolocating bats 43.70 3.77735 6.65801 0 1 0
2 628.0 non-echolocating bats 34.80 3.54962 6.44254 0 1 0
3 258.0 non-echolocating bats 23.30 3.14845 5.55296 0 1 0
4 315.0 non-echolocating bats 22.40 3.10906 5.75257 0 1 0
5 24.3 non-echolocating birds 2.46 0.90016 3.19048 0 0 1
6 35.0 non-echolocating birds 3.93 1.36864 3.55535 0 0 1
7 72.8 non-echolocating birds 9.15 2.21375 4.28772 0 0 1
8 120.0 non-echolocating birds 13.80 2.62467 4.78749 0 0 1
9 213.0 non-echolocating birds 14.60 2.68102 5.36129 0 0 1
10 275.0 non-echolocating birds 22.80 3.12676 5.61677 0 0 1
11 370.0 non-echolocating birds 26.20 3.26576 5.91350 0 0 1
12 384.0 non-echolocating birds 25.90 3.25424 5.95064 0 0 1
13 442.0 non-echolocating birds 29.50 3.38439 6.09131 0 0 1
14 412.0 non-echolocating birds 43.70 3.77735 6.02102 0 0 1
15 330.0 non-echolocating birds 34.00 3.52636 5.79909 0 0 1
16 480.0 non-echolocating birds 27.80 3.32504 6.17379 0 0 1
17 93.0 echolocating bats 8.83 2.17816 4.53260 1 0 0
18 8.0 echolocating bats 1.35 0.30010 2.07944 1 0 0
19 6.7 echolocating bats 1.12 0.11333 1.90211 1 0 0
20 7.7 echolocating bats 1.02 0.01980 2.04122 1 0 0
MODEL 1:
Regression Analysis: LN(Energy) versus ebat, bird
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 17.844 8.9222 12.50 0.000
ebat 1 15.051 15.0511 21.09 0.000
bird 1 1.112 1.1118 1.56 0.229
Error 17 12.130 0.7135
Total 19 29.975
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.844718 59.53% 54.77% 45.06%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 3.396 0.422 8.04 0.000
ebat -2.743 0.597 -4.59 0.000 1.60
bird -0.609 0.488 -1.25 0.229 1.60
Regression Equation
LN(Energy) = 3.396 - 2.743 ebat - 0.609 bird
Fits and Diagnostics for Unusual Observations
Obs LN(Energy) Fit Resid Std Resid
5 0.900 2.787 -1.887 -2.33 R
17 2.178 0.653 1.525 2.09 R
R Large residual
MODEL 2:
Regression Analysis: LN(Energy) versus LN(Mass)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 29.3919 29.3919 907.64 0.000
LN(Mass) 1 29.3919 29.3919 907.64 0.000
Error 18 0.5829 0.0324
Total 19 29.9748
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.179952 98.06% 97.95% 97.65%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -1.468 0.137 -10.70 0.000
LN(Mass) 0.8086 0.0268 30.13 0.000 1.00
Regression Equation
LN(Energy) = -1.468 + 0.8086 LN(Mass)
Fits and Diagnostics for Unusual Observations
Std
Obs LN(Energy) Fit Resid Resid
14 3.7773 3.4004 0.3769 2.18 R
R Large residual
MODEL 3:
Regression Analysis: LN(Energy) versus ebat, bird, LN(Mass)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 29.4215 9.8072 283.59 0.000
ebat 1 0.0052 0.0052 0.15 0.703
bird 1 0.0277 0.0277 0.80 0.384
LN(Mass) 1 11.5770 11.5770 334.77 0.000
Error 16 0.5533 0.0346
Total 19 29.9748
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.185963 98.15% 97.81% 97.30%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -1.576 0.287 -5.49 0.000
ebat 0.079 0.203 0.39 0.703 3.80
bird 0.102 0.114 0.90 0.384 1.81
LN(Mass) 0.8150 0.0445 18.30 0.000 2.58
Regression Equation
LN(Energy) = -1.576 + 0.079 ebat + 0.102 bird + 0.8150 LN(Mass)
MODEL 4:
Regression Analysis: LN(Energy) versus ebat, bird, LN(Mass), ebat*LN(Mass), bird*LN(Mass)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 5 29.4699 5.89399 163.44 0.000
ebat 1 0.0351 0.03509 0.97 0.341
bird 1 0.0408 0.04084 1.13 0.305
LN(Mass) 1 0.2952 0.29520 8.19 0.013
ebat*LN(Mass) 1 0.0333 0.03330 0.92 0.353
bird*LN(Mass) 1 0.0477 0.04775 1.32 0.269
Error 14 0.5049 0.03606
Total 19 29.9748
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.189900 98.32% 97.71% 96.29%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -0.20 1.26 -0.16 0.875
ebat -1.27 1.29 -0.99 0.341 146.62
bird -1.38 1.30 -1.06 0.305 223.30
LN(Mass) 0.590 0.206 2.86 0.013 52.97
ebat*LN(Mass) 0.215 0.224 0.96 0.353 37.56
bird*LN(Mass) 0.246 0.213 1.15 0.269 180.67
Regression Equation
LN(Energy) = -0.20 - 1.27 ebat - 1.38 bird + 0.590 LN(Mass) + 0.215 ebat*LN(Mass)
+ 0.246 bird*LN(Mass)
Fits and Diagnostics for Unusual Observations
Std
Obs LN(Energy) Fit Resid Resid
17 2.178 2.177 0.001 0.15 X
X Unusual X
Explanation / Answer
1. The estimated slope and intercept for non-echo locating bats are:
Intercept: -0.2025
Slope:0.5898
The estimated slope and intercept for non echo locating birds are:
Intercept: -1.58085
Slope: 0.83537
The estimated value of slope and intercept for echo locating bats are:
Intercept:-1.4705
Slope:0.8047.
1.b. The value of the regression co efficients when the model is refitted with the indicator variables nbat and bird are are given as follows:
Intercept: -1.49770
LN.Mass : 0.81496
Bird : 0.02359
nebat: -0.07869
The regression equation is given as follows:
LN.energy = -1.49770 + 0.81496*LN.Mass +0.02359*Bird -0.07869*nebat.
1.c. The coefficient of log energy vs log mass for three species taken together is given below:
Slope: -1.468
Intercept: 0.8086
1.d. The regression line for non-echo locating birds is:
y = -1.58085 + 0.83537*x
The regression line for echo locating bats is:
y = -1.4705 + 0.8047*x.
The regression lines for echo locating bats and non echo locating birds are not similar.
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