The following table shows the length, in meters, of the winning long jump in the Olympic Games for the indicated year. (One meter is 39.37 inches.) Year 1900 1904 1908 1912 Length 7.19 7.34 7.48 7.60 (a) Find the equation of the regression line that gives the length as a function of time. (Let t be the number of years since 1900 and L the length of the wining long jump, in meters. Round the regression lin
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The following table shows the length, in meters, of the winning long jump in the Olympic Games for the indicated year. (One meter is 39.37 inches.)
| Year | 1900 | 1904 | 1908 | 1912 |
|---|---|---|---|---|
| Length | 7.19 | 7.34 | 7.48 | 7.60 |
(b) Explain in practical terms the meaning of the slope of the regression line.
(c) Plot the data points and the regression line.
(d) Would you expect the regression line formula to be a good model of the winning length over a long period of time?
Explain your reasoning.
(e) There were no Olympic Games in 1916 because of World War I, but the winning long jump in the 1920 Olympic Games was 7.15 meters. Compare this with the value that the regression line model gives. Is the result consistent with your answer to part (d)?
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