The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained. Systolic Blood pressue X1 132 Age (years) X2 52 Weight (pounds) Хз 173 143 59 184 153 67 194 162 73 211 154 64 196 220 188 168 74 137 54 149 61 188 159 65 207 128 166 46 167 72 217
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.
(a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation for each variable. (Use 2 decimal places.)
| x | s | CV | |
| x1 | % | ||
| x2 | % | ||
| x3 | % |
(b)For each pair of variables, generate the
| r | r2 | |
| x1, x2 | ||
| x1, x3 | ||
| x2, x3 |
(c)What percent of the variation in x1 can be explained by the corresponding variation in x2? Answer the same question for x3. (Use 1 decimal place.)
| x2 | % |
| x3 | % |
Perform a
%
Look at the coefficients of the regression equation. Write out the regression equation. (Use 3 decimal places.)
| x1 = | + x2 | + x3 |
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