Movement Analysis Table: Shoulder Push Press
Movement
Type
(i.e. flexion Movement Plane
extension
etc.)
Movement
Axis
Type of Contraction
(concentric, eccentric,
isometric)
Muscles Involved
Rectus femoris
Vastus lateralis
Vastus medius
Vastus intermeduis
In order to design a training program best fitted to my needs, I need to consider what my goals. My goals are to increase both
my strength and muscular endurance, as well as improving my physical appearance; therefore, my training program needs to
include
1. How do you feel about your overall nutrition and physical activity levels based on what
you have recorded over the past week? What have you learned from tracking your diet and
physical activity levels?
Based on what I have reviewed from the recordings
1. Which of the following is/are properties of life? A) cellular organization
B) DNA
C) the ability to take in energy and molecules and use them
(metabolism) D) the ability to reproduce
E) Allofthechoicesabovearecorrect.
2. Generally speaking, there are j
Module 5 (Chapter 6)
A HIGH QUALITY protein is best described as one that:
Select one:
a. contains 10 grams of protein per 100 grams of food
b. contains all of the essential amino acids in the proper amounts and ratio
c. contains all of the nonessential a
WHAT HUMANITIES IS FOR ME?
The calling of Humanities is to make us truly human in the best sense of the world.
A famous quote written by an American patron of modern architecture and a lay leader
in the Christian ecumenical and civil rights, namely, Josep
ANALYSIS OF VARIANCE AND COVARIANCE
161
by replacing m with m0. For the SBPs before the exercise program in Example 11.4,
95 percent confidence limits for are 15 13 4 242 15 13 + 9 4 242 = 0 204 and
(15.13 0.025)/[15.13 + 9(0.025)] = 0.984.
11.8
Analysis
140
REGRESSION AND CORRELATION
Now,
logit p x1 + 1, x2 logit p x1 , x2
= ln
p x1 + 1, x2
1 p x1 + 1, x2
p x1 , x2
1 p x 1 , x2
(10.54b)
= 1
Thus, the odds ratio of Y for one unit change in X1 is e 1 . Similarly, its odds ratio
for one unit change in X2 be
138
10.8
REGRESSION AND CORRELATION
Logistic regression and the odds ratio
The response, success and failure, of a treatment can be represented by the random
variable Y taking the values of one (1) and zero (0) respectively, with the probabilities
P Y = 1
136
REGRESSION AND CORRELATION
The estimate of the intercept coefficient is 91.07 with the sample S.E. of 36.85.
The null hypothesis H0 0 = 0 for the intercept is also rejected with the p-value
of 0.043.
Although, the above test for the intercept shows th
ANALYSIS OF VARIANCE AND COVARIANCE
Table 11.3
169
Expected values of the mean squares. Randomized blocks design.
Source
d.f.
MS
E(MS)
Blocks
(b 1)
MB
2 + t
b
i=1
t
Treatments
(t 1)
MT
2 + b
Error
(b 1) (t 1)
ME
2
2i b 1
2j t 1
j=1
The right-hand side exp
144
REGRESSION AND CORRELATION
As an example, to test H0 12 = 0 5 versus 12 0 5 for the correlation of
age and weight, z = (1/2)ln[(1 + 0.74)/(1 0.74)] = 0.9505, and E z = 1 2
ln 1 + 0 5 1 0 5 = 0 5493. Now, Z = 0 9505 0 5493 17 1 2 = 1 65, with the
p-val
ANALYSIS OF VARIANCE AND COVARIANCE
163
11.8.2 Tests of hypotheses for the slope coefficient and equality of
the means
The null hypothesis to examine whether the response yij significantly depends on the
covariate xij is H0 = 0. The statistic for this hyp
176
ANALYSIS OF VARIANCE AND COVARIANCE
adults are observed for each combination of the weight and fitness factors, the row
and column classifications. Similarly, the effects of weight and diet on hypertension
or lipid levels can be studied through a cros
150
REGRESSION AND CORRELATION
n
Yi 0 1 X1i 2 X2i p Xpi = 0,
1
n
Yi 0 1 X1i 2 X2i p Xpi X1i = 0,
1
n
Yi 0 1 X1i 2 X2i p Xpi X2i = 0,
1
n
Yi 0 1 X1i 2 X2i p Xpi X2i = 0
1
The estimators for the regression coefficients are given by = X X 1 X Y. They
are unb
162
ANALYSIS OF VARIANCE AND COVARIANCE
with respect to and i. This minimization results in the estimators
k
m
k
=
m
xij xi yij yi
i=1 j=1
xij xi
2
(11.35)
i=1 j=1
i = yi xi x
(11.36)
i j = i j = yi yj xi xj
(11.37)
and
The Total, Between and Within Sum o
REGRESSION AND CORRELATION
n1
Yi 0 1 X1i p Xpi
2
1
2 =
147
(10.68)
n n2 + p + 1
The degrees of freedom in the denominator is the same as (n1 p 1). This estimate
for 2 is the same as the estimate obtained from the regression of Y on (X1, X2, , Xp)
with the
172
ANALYSIS OF VARIANCE AND COVARIANCE
11.12 Latin squares
The Randomized Blocks design described in Section (11.10) is a two-way classification. In the illustration considered, differences between the treatments are analyzed
after adjusting for the diff
ANALYSIS OF VARIANCE AND COVARIANCE
175
Example 11.12 For the observations in Table 11.7, the number of assignments of
the three treatments to each of the three patients are m = 2. The overall total for
the t2m =18 observations is G =245 and C.F = 2452/18
REGRESSION AND CORRELATION
139
10.8.1 A single continuous predictor
At the value of x for the predictor, logit p x = 0 + 1 x. At (x + 1), logit p x + 1
= 0 + 1 x + 1 . With this model,
logit p x + 1 logit p x = ln
p x+1
1p x + 1
px
1p x
= 1
(10.52a)
and t
164
ANALYSIS OF VARIANCE AND COVARIANCE
Table 11.2
Source
Between
Within
Total
Sums of Squares and Cross Products for the Analysis of Covariance.
d.f
x
y
xy
SS and d.f. under H0 i = 0
k1
nk
n1
Bxx
Wxx
Txx
Byy
Wyy
Tyy
Bxy
Wxy
Txy
2 = Wy x n k 1 .
2
Wy x =
REGRESSION AND CORRELATION
151
The estimates v 0 , v 1 , v 2 , ,v p 1 for the variances of the regression
coefficients, their covariances, and v(i) for the variance in (A10.2) are obtained
by substituting 2 for 2.
A10.3 Expression for SSR in (10.38)
The S
166
ANALYSIS OF VARIANCE AND COVARIANCE
These estimators become
k
ni
ni
k
=
xij xi yij yi
1
xij xi
1
2
(11.50)
1
1
i = yi xi x
(11.51)
i j = yi yj xi xj
(11.52)
and
In these expressions xi , yi are the means of the k treatments. These three estimators are
REGRESSION AND CORRELATION
133
ANOVA Table for the regression of LDL on weight for the two groups with a
dummy variable.
Source
d.f
SS
MS
F
p-value
Regression
Residual
Total
3
16
19
1758.12
874.68
2632.80
586.04
54.67
10.72
0.0004
With d = 1, the intercep
134
REGRESSION AND CORRELATION
ANOVA Table.
Source
d.f
SS
MS
F
p-value
Regression
Residual
Total
2
17
19
1674.73
958.07
2632.80
8373.6
56.36
14.86
0.0013
The estimate of the common slope coefficient is 0.99 with the S.E. of 0.26,with
t17 = 0 99 0 26 = 3 8
148
REGRESSION AND CORRELATION
XY are the variance of X and covariance of (X, Y) respectively. Thus, errors in the
predictor should be avoided.
Exercises
Sample observations from Table T10.1(ac) are used for Exercises 10.1010.14.
Age, weight and Fitness
ANALYSIS OF VARIANCE AND COVARIANCE
171
hypothesis is F = MT ME , which follows the F-distribution with [(t 1), (t 1)(b 1)]
d.f. The patient effect i is considered random with E i = 0 and V i = 2 . The test
statistic for the hypothesis H0 2 = 0 becomes F
REGRESSION AND CORRELATION
143
respectively, as presented in Table T10.1(c), the estimates from the sample of 20 units
are r12 = 0 74, r13 = 0 82 and r23 = 0 42. Although age and weight are positively
correlated, fitness is negatively correlated with both