The mean height of American women in their twenties is about 64.3 inches, and the standard deviation is about 3.9 inches. The mean height of men the same age is about 69.9 inches, with standard deviation about 3.1 inches. Suppose that the correlation between the heights of husbands and wives is about r 0.5. (a) What are the slope and intercept of the regression line of the husband’s height on the wife’s height in young couples? (b) Draw a graph of this regression line for heights of wives between 56 and 72 inches. Predict the height of the husband of a woman who is 67 inches tall, and plot the wife’s height and predicted husband’s height on your graph. (c) You don’t expect this prediction for a single couple to be very accurate. Why not?
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 mean height of American
women in their twenties is about 64.3 inches, and the standard deviation is about 3.9 inches. The mean height of men
the same age is about 69.9 inches, with standard deviation
about 3.1 inches. Suppose that the
heights of husbands and wives is about r 0.5.
(a) What are the slope and intercept of the regression
line of the husband’s height on the wife’s height in young
couples?
(b) Draw a graph of this regression line for heights of wives
between 56 and 72 inches. Predict the height of the husband
of a woman who is 67 inches tall, and plot the wife’s height
and predicted husband’s height on your graph.
(c) You don’t expect this prediction for a single couple to be
very accurate. Why not?
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