Reading Minitab output for a simple linear regression model
Regression Analysis: Height versus Mother Height
The regression equation is
Height = 24.7 + 0.640 Mother Height
(dependent
variable, y)
(intercept,
b0 )
Predictor
Constant
Mother H
(slope,
b1)
the estimated regression
equation: y = b0 + b1x
(independent
variable, x)
(estimates)
(sd of ests.)
(test
statistics)
(p-values)
Coef
24.690
0.6405
SE Coef
8.978
0.1394
T
2.75
4.59
P
0.009
0.000
intercept, b0
slope, b1
tests H0: β0 = 0, vs. two-tailed alternative
tests H0: β1 = 0, vs. two-tailed alternative
(the latter is equivalent to testing for
linear correlation between x and y)
S = 2.973
R-Sq = 35.7%
R-Sq(adj) = 34.0%
(standard error
of estimate, se)
(coefficient of linear
determination, r2)
(adjusted r2, used for multiple regression)
(the coefficient of linear
correlation is the square root
of r2, with the same sign as the
slope, b1)
for a simple linear regression
model, these tests are equivalent
Analysis of Variance
(test stat.)
Source
Regression
Residual Error
Total
DF
1
38
39
SS
186.54
335.76
522.30
MS
186.54
8.84
F
21.11
(p-value)
P
0.000
tests for overall model fit
(used for multiple regression)
“explained variation”
“unexplained variation”
“total variation”
(total df = n-1
for simple linear
regression)
Unusual Observations
Obs
8
21
30
(observed x)
(observed y)
Mother H
63.0
63.0
75.0
Height
71.000
58.600
71.100
(ŷ: predicted value of y
for the observed x)
Fit
65.039
65.039
72.724
sŷ
(y – ŷ)
SE Fit
0.505
0.505
1.560
Residual
5.961
-6.439
-1.624
(y – ŷ)
se
St Resid
2.03R
-2.20R
-0.64 X
R denotes an observation with a large standardized residual
(Standardized residuals are residuals divided by se; they have a mean of 0 and a standard deviation of 1. This simplifies determining
how far an observed value is from the least-squares regression line, relative to the dispersion of observations around the line.
Observations with standardized residuals greater than +2 or less than –2 are considered “unusual” by Minitab.)
X denotes an observation whose X value gives it large influence.
(Observations with x values far from the mean of x have a greater impact on model parameters – such observations are said to have
high leverage. Removing such observations (which may not be warranted!) would produce substantially different parameter estimates
of the slope and intercept.)