Have your calculator find the linear regression for the roller coaster data above. Write the linear model, clearly define the variables and state correlation coefficient and clearly interpret the slope. Use the model to find the drop height that will result in a coaster speed of 150 kph.
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.
Roller coasters get their speed as a result of dropping down a steep incline. The table below gives height of a drop and the speed achieved for different roller coasters around the world.
|
Drop in Meters (m |
25 |
30 |
28 |
58 |
55 |
40 |
90 |
100 |
|
Speed of the coaster (k.p.h) |
80 |
90 |
78 |
93 |
90 |
93 |
105 |
128 |
Have your calculator find the linear regression for the roller coaster data above. Write the linear model, clearly define the variables and state
Use the model to find the drop height that will result in a coaster speed of 150 kph.
Have your calculator find the exponential regression for this data. Write the exponential model, clearly define the variables and state correlation coefficient.
Use the model to find the drop height that will result in a coaster speed of 150 kph.
e) Which model is the better fit for the data? Why
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