# Normal Distribution and Min 1q Median

**Topics:**Errors and residuals in statistics, Normal distribution, Degrees of freedom

**Pages:**149 (31871 words)

**Published:**March 18, 2013

> model1=lm(S~u_direction+mx+my+mz,data)

> summary(model1)

Call:

lm(formula = S ~ u_direction + mx + my + mz, data = data)

Residuals:

Min 1Q Median 3Q Max

-11.8430 -0.3962 0.3252 0.7887 18.3963

Coefficients:

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

(Intercept) -0.50372 0.12738 -3.955 7.93e-05 ***

u_direction -0.40368 0.07996 -5.048 4.85e-07 ***

mx -0.40573 0.01292 -31.404 < 2e-16 ***

my -0.25862 0.01292 -20.018 < 2e-16 ***

mz -0.36557 0.01292 -28.296 < 2e-16 ***

---

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

Residual standard error: 1.809 on 2043 degrees of freedom

Multiple R-squared: 0.8874, Adjusted R-squared: 0.8872

F-statistic: 4026 on 4 and 2043 DF, p-value: < 2.2e-16

> data=read.table("d:/111113/2.txt",header=T)

Call:

lm(formula = S ~ u_direction + mx + my + mz, data = data)

Residuals:

Min 1Q Median 3Q Max

-11.0966 -0.6784 0.3573 1.0221 15.9857

Coefficients:

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

(Intercept) -1.16784 0.31215 -3.741 0.000188 ***

u_direction -0.18336 0.08816 -2.080 0.037656 *

mx -0.43009 0.01424 -30.195 < 2e-16 ***

my -0.25563 0.01424 -17.947 < 2e-16 ***

mz -0.29883 0.01424 -20.979 < 2e-16 ***

---

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

Residual standard error: 1.995 on 2043 degrees of freedom

Multiple R-squared: 0.8557, Adjusted R-squared: 0.8554

F-statistic: 3028 on 4 and 2043 DF, p-value: < 2.2e-16

> data=read.table("d:/111113/2.txt",header=T)

> model1=lm(S~u_direction+mx+my+mz,data)

> summary(model1)

Call:

lm(formula = S ~ u_direction + mx + my + mz, data = data)

Residuals:

Min 1Q Median 3Q Max

-11.4155 -0.5540 0.3551 0.9190 17.8925

Coefficients:

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

(Intercept) -0.72664 0.21670 -3.353 0.000813 ***

u_direction -0.32031 0.08475 -3.779 0.000162 ***

mx -0.41581 0.01369 -30.364 < 2e-16 ***

my -0.25715 0.01369 -18.778 < 2e-16 ***

mz -0.32750 0.01369 -23.916 < 2e-16 ***

---

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

Residual standard error: 1.918 on 2043 degrees of freedom

Multiple R-squared: 0.8688, Adjusted R-squared: 0.8685

F-statistic: 3381 on 4 and 2043 DF, p-value: < 2.2e-16

> data=read.table("d:/111113/4.txt",header=T)

> summary(data)

mx my mz Face Min. :1.000e-09 Min. :1.000e-09 Min. :1.000e-09 Min. :0.00 1st Qu.:1.000e-02 1st Qu.:1.000e-02 1st Qu.:1.000e-02 1st Qu.:1.75 Median :5.000e-02 Median :6.250e-02 Median :6.250e-02 Median :3.50 Mean :1.905e+00 Mean :1.906e+00 Mean :1.906e+00 Mean :3.50 3rd Qu.:1.000e-01 3rd Qu.:2.000e-01 3rd Qu.:2.000e-01 3rd Qu.:5.25 Max. :2.000e+01 Max. :2.000e+01 Max. :2.000e+01 Max. :7.00 u_direction S

Min. :4.0 Min. :-18.0000

1st Qu.:4.0 1st Qu.: -3.5033

Median :4.5 Median : -1.8899

Mean :4.5 Mean : -3.7923

3rd Qu.:5.0 3rd Qu.: -1.0264

Max. :5.0 Max. : 0.2751

> model1=lm(S~u_direction+mx+my+mz,data)

> summary(model1)

Call:

lm(formula = S ~ u_direction + mx + my + mz, data = data)

Residuals:

Min 1Q Median 3Q Max

-11.135 -0.810 0.331 1.048 9.935

Coefficients:

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

(Intercept) -1.80483 0.42020 -4.295 1.83e-05 ***

u_direction -0.02980 0.09272 -0.321 0.748

mx -0.41383 0.01498 -27.623 < 2e-16 ***

my -0.26668 0.01498 -17.801...

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