Compare AIC against model1: comment on the coefficients AIC: Start: AIC=100.48 T

Question

Compare AIC against model1: comment on the coefficients

AIC:

Start: AIC=100.48
TotalSleep ~ BodyWt + BrainWt + LifeSpan + Gestation + Predation +
    Exposure + Danger

            Df Sum of Sq    RSS     AIC
- BrainWt    1     0.728 314.63 98.577
- LifeSpan   1     0.916 314.82 98.602
- BodyWt     1     5.822 319.73 99.252
- Exposure   1     6.729 320.64 99.371
<none>                   313.91 100.480
- Predation 1    41.446 355.35 103.689
- Gestation 1    67.056 380.96 106.611
- Danger     1   103.267 417.17 110.425

Step: AIC=105.14
TotalSleep ~ BodyWt + LifeSpan + Gestation + Predation + Exposure +
    Danger

Call:
lm(formula = TotalSleep ~ BodyWt + LifeSpan + Gestation + Predation +
    Exposure + Danger, data = mammals2)

Coefficients:
(Intercept)       BodyWt     LifeSpan    Gestation   Predation2   Predation3
15.213829     0.002478    -0.014815    -0.019560     4.535830     6.648566
Predation4   Predation5    Exposure2    Exposure3    Exposure4    Exposure5
   9.959651     9.277683    -0.616353    -0.810158     1.043284     1.506158
    Danger2      Danger3      Danger4      Danger5
-5.802218   -11.141607   -12.655999   -17.867224

> model1.AIC <- stepAIC(model1)
Start: AIC=100.48
TotalSleep ~ BodyWt + BrainWt + LifeSpan + Gestation + Predation +
    Exposure + Danger

            Df Sum of Sq    RSS     AIC
- BrainWt    1     0.728 314.63 98.577
- LifeSpan   1     0.916 314.82 98.602
- BodyWt     1     5.822 319.73 99.252
- Exposure   1     6.729 320.64 99.371
<none>                   313.91 100.480
- Predation 1    41.446 355.35 103.689
- Gestation 1    67.056 380.96 106.611
- Danger     1   103.267 417.17 110.425

Step: AIC=105.14
TotalSleep ~ BodyWt + LifeSpan + Gestation + Predation + Exposure +
    Danger

> summary(model1.AIC)

Call:
lm(formula = TotalSleep ~ BodyWt + LifeSpan + Gestation + Predation +
    Exposure + Danger, data = mammals2)

Residuals:
    Min      1Q Median      3Q     Max
-5.9407 -1.2994 -0.0737 0.8871 6.5839

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept) 15.213829   1.595008   9.538 5.62e-10 ***
BodyWt        0.002478   0.002145   1.156 0.25831   
LifeSpan     -0.014815   0.037346 -0.397 0.69484   
Gestation    -0.019560   0.008146 -2.401 0.02378 *
Predation2    4.535830   2.285956   1.984 0.05788 .
Predation3    6.648566   3.512354   1.893 0.06955 .
Predation4    9.959651   4.300563   2.316 0.02871 *
Predation5    9.277683   4.628750   2.004 0.05555 .
Exposure2    -0.616353   1.621361 -0.380 0.70693   
Exposure3    -0.810158   2.460643 -0.329 0.74461   
Exposure4     1.043284   3.236826   0.322 0.74979   
Exposure5     1.506158   4.951755   0.304 0.76342   
Danger2      -5.802218   2.365976 -2.452 0.02122 *
Danger3     -11.141607   3.473850 -3.207 0.00354 **
Danger4     -12.655999   4.866172 -2.601 0.01514 *
Danger5     -17.867224   6.624647 -2.697 0.01211 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.036 on 26 degrees of freedom
Multiple R-squared: 0.7365,    Adjusted R-squared: 0.5844
F-statistic: 4.844 on 15 and 26 DF, p-value: 0.0002236

model1:

Call:

lm(formula = TotalSleep ~ BodyWt + BrainWt + LifeSpan + Gestation +

    Predation + Exposure + Danger, data = mammals2)

Residuals:

    Min      1Q Median      3Q     Max

-6.2292 -1.8823 -0.1445 1.8914 5.9885

Coefficients:

              Estimate Std. Error t value Pr(>|t|)   

(Intercept) 17.1091251   1.3363885 12.803 1.47e-14 ***

BodyWt       0.0047024   0.0059218   0.794 0.43266   

BrainWt     -0.0009979   0.0035541 -0.281 0.78059   

LifeSpan    -0.0145760 0.0462766 -0.315 0.75471   

Gestation   -0.0188108   0.0069799 -2.695 0.01086 *

Predation    2.3151350 1.0926906   2.119   0.04150 *

Exposure     0.5844391 0.6845807   0.854   0.39924   

Danger      -4.5375726 1.3567624 -3.344   0.00202 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.039 on 34 degrees of freedom

Multiple R-squared: 0.6548,    Adjusted R-squared: 0.5837

F-statistic: 9.213 on 7 and 34 DF, p-value: 2.398e-06

Explanation / Answer

the error of an observed value is the deviation of observed value from the true value of a quantity of and the residual of an observed value is the difference between the observed value and estimated value of the quantity of interest. 3.039 is the residual standard error it is also called regression errors and regression residuals

the number of degrees of freedom is the number of values in final calculation of a statistic that are free to change. the number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom.

R squared values are not always bad and high R squared values are not always good.. R squared is a statistical meausre of how close the data are to the fitted regression line. it is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.  

R squared= explained variation/total variation.

R-squared is always between 0 and 100%

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