The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals. Descriptive Statistics Variable N Mean Median TrMean StDev SE Mean x1 15 158.42 158.72 158.42 3.127 0.807388 x2 15 65.95 66.45 65.95 1.091 0.281695 x3 15 187.23 186.63 187.23 4.171 1.076948 Variable Minimum Maximum Q1 Q3 x1 124 174 135.828 166.400 x2 41 80 47.088 77.579 x3 124 244 142.885 223.525 Correlations (Pearson) x1 x2 x2 0.829 x3 0.860 0.661 Regression Analysis The regression equation is x1 = 0.837 + 1.120x2 + 0.928x3 Predictor Coef StDev T P Constant 0.837 0.737 1.14 0.139 x2 1.120 0.589 1.90 0.041 x3 0.928 0.716 1.30 0.110 S = 0.221 R-sq = 90.3 % R-sq(adj) = 95.1 % Given the correlation coefficient for all pairs, which pair shows the strongest influence?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following
|
Descriptive Statistics |
||||||
|
Variable |
N |
Mean |
Median |
TrMean |
StDev |
SE Mean |
|
x1 |
15 |
158.42 |
158.72 |
158.42 |
3.127 |
0.807388 |
|
x2 |
15 |
65.95 |
66.45 |
65.95 |
1.091 |
0.281695 |
|
x3 |
15 |
187.23 |
186.63 |
187.23 |
4.171 |
1.076948 |
|
Variable |
Minimum |
Maximum |
Q1 |
Q3 |
|
x1 |
124 |
174 |
135.828 |
166.400 |
|
x2 |
41 |
80 |
47.088 |
77.579 |
|
x3 |
124 |
244 |
142.885 |
223.525 |
|
Correlations (Pearson) |
||
|
|
x1 |
x2 |
|
x2 |
0.829 |
|
|
x3 |
0.860 |
0.661 |
Regression Analysis
The regression equation is
x1 = 0.837 + 1.120x2 + 0.928x3
|
Predictor |
Coef |
StDev |
T |
P |
|
Constant |
0.837 |
0.737 |
1.14 |
0.139 |
|
x2 |
1.120 |
0.589 |
1.90 |
0.041 |
|
x3 |
0.928 |
0.716 |
1.30 |
0.110 |
|
S = 0.221 |
R-sq = 90.3 % |
R-sq(adj) = 95.1 % |
|
|
Given the
The pair, x1 and x3 are better.
As the table suggests:
| x1 | x2 | |
| x1 | 0.829 | - |
| x3 | 0.860 | 0.6661 |
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