Age of Bus (years) Annual Maintenance Cost ($) 1 350 2 370 2 480 2 520 590 550 3 4 750 4 800 790 5 950
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 regional transit authority for a major metropolitan area wants to determine whether
there is a relationship between the age of a bus and the annual maintenance cost. A sample
of ten buses resulted in the following data:
a. Develop a scatter chart for these data. What does the scatter chart indicate about the
relationship between age of a bus and the annual maintenance cost?
b. Use the data to develop an estimated regression equation that could be used to predict
the annual maintenance cost given the age of the bus. What is the estimated regression
model?
c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05
level of significance. What are the correct interpretations of the estimated regression
parameters? Are these interpretations reasonable?
d. How much of the variation in the sample values of annual maintenance cost does the
model you estimated in part b explain?
e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?
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