The following table gives the gold medal times for every other Summer Olympics for the women’s 100-meter freestyle (swimming). a.Decide which variable should be the independent variable and which should be the dependent variable. b. Draw a scatter plot of the data. c. Does it appear from inspection that there is a relationship between the variables? Why or why not? d. Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. e. Find the correlation coefficient. Is the decrease in times significant? f. Find the estimated gold medal time for 1932. Find the estimated time for 1984. g. Why are the answers from part f different from the chart values? h. Does it appear that a line is the best way to fit the data? Why or why not? i. Use the least-squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your answer is reasonable? Why or why not?
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 gives the gold medal times for every other Summer Olympics for the women’s 100-meter freestyle (swimming).
a.Decide which variable should be the independent variable and which should be the dependent variable.
b. Draw a
c. Does it appear from inspection that there is a relationship between the variables? Why or why not?
d. Calculate the least squares line. Put the equation in the form of: ŷ = a + bx.
e. Find the
f. Find the estimated gold medal time for 1932. Find the estimated time for 1984.
g. Why are the answers from part f different from the chart values?
h. Does it appear that a line is the best way to fit the data? Why or why not?
i. Use the least-squares line to estimate the gold medal time for the next Summer Olympics. Do you think that your answer is reasonable? Why or why not?
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