a) Draw a scatter diagram of the data. b) Find the least squares regression line of number of freight tonnes (in millions) carried on a year. (Note: Use only the last two digits of the year). c) Draw the line in (b) on the scatter diagram in (a). Comment on whether you feel the line is a good fit of the data. d) Use the line in (b) to predict the number of freight tonnes that might be carried in Australia in both 2020 and 2025. e) Do you think your predictions in (d) will be relatively accurate? 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.
Assume that the table below displays the number of freight tonnes carried (in millions) in Australia between 1990 and 2015.
Year
1990
1995
2000
2005
2010
2015
Number of freight tonnes (millions)
66
84
104
126
160
186
a) Draw a
b) Find the least squares regression line of number of freight tonnes (in millions) carried on a year. (Note: Use only the last two digits of the year).
c) Draw the line in (b) on the scatter diagram in (a). Comment on whether you feel the line is a good fit of the data.
d) Use the line in (b) to predict the number of freight tonnes that might be carried in Australia in both 2020 and 2025.
e) Do you think your predictions in (d) will be relatively accurate? Why or why not?
Step by step
Solved in 3 steps with 2 images
