53.1 Find the equation of the least-squares line. Identify and interpret the slope and the y – intercept. Slope: -0.27556 Find the correlation coefficient and interpret. Correlation Coefficient: -.95112 Determine if there is a significant correlation between the gold medal time and the year of the Summer Olympics. Explain your reasoning. There is a strong negative linear relationship
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.
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A statistician is curious if the gold medal time for the women's 100 - meter freestyle depends upon the year that the Summer Olympics took place. A sample of every other Summer Olympics for the women's 100-meter freestyle produced the following data:
Year
1912
1924
1932
1952
1960
1968
1976
1984
1992
2000
2008
Time (in seconds)
82.2
72.4
66.8
66.8
61.2
60.0
55.65
55.92
54.64
53.8
53.1
Find the equation of the least-squares line. Identify and interpret the slope and the y – intercept.
Slope: -0.27556
Find the
Correlation Coefficient: -.95112
Determine if there is a significant correlation between the gold medal time and the year of the Summer Olympics. Explain your reasoning.
There is a strong negative linear relationship
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