ou run a regression for Y using a single X variable, where the sample mean of X is 20.5 and the sum of squared deviations of the X values from their mean is 196.0. The sample size is 50, and the standard error of estimate in the regression output is 157.5. Now you want to predict Y when X equals 25.5. Which of the following is the most accurate? a. The standard error of the prediction of an individual Y value when X = 25.5 is about 60.5. b. The standard error of the prediction of an individual Y value when X = 25.5 is about 168.7. c. Prediction in this case is risky. It amounts to extrapolation because an X value of 25.5 is about five standard deviations from the mean of 20.5. d. The standard error of the prediction of the mean of Y when X = 25.5 is about 22.3.
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.
You run a regression for Y using a single X variable, where the sample mean of X is 20.5 and the sum of squared deviations of the X values from their mean is 196.0. The
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