20,000 10,000 10,000 -20,000 30,000 40,000 50,000 60,000 70,000 Predicted ($) 20,000 10,000 -10,000 -20,000 Normal Scores Residuals (S) Residuals ($)
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.
Education vs. income The following displays examine
the
for several U.S. cities.
Education 57 10.9509 0.848344
Income 57 32742.6 3618.01
Dependent variable is: Income
R-squared = 32.9%
s = 2991 with 57 - 2 = 55 degrees of freedom
Variable Coefficient SE(Coeff) t-ratio P-value
Intercept 5970.05 5175 1.15 0.2537
Education 2444.79 471.2 5.19 ...0.0001
a) Do you think the assumptions for inference are met?
Explain.
cation and income levels in these cities?
or the same if data were plotted for individual people
rather than for cities in aggregate? Explain.
d) Create and interpret a 95% confidence interval for the
slope of the true line that describes the association
between income and education.
e) Predict the median income for cities where residents
spent an average of 11 years in school. Describe your
estimate with a 90% confidence interval, and interpret
that result.
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