Listed below are repair costs (in dollars) for cars crashed at 6mi/h in full-front crash tests and the same cars crashed at 6mi/h in full-rear crash tests (based on data from the Insurance Institute for Highway Safety). The cars are Toyota Camry, Mazda 6, Volvo S40, Saturn Aura, Subaru Legacy, Hyundai Sonata, and Honda Accord. Front 936 978 2252 1032 3911 4312 3469 Rear 1480 1202 802 3191 1122 739 2767 a) Is there sufficient evidence to conclude that there is a linear correlation between the repair costs from full-front crashes and full-rear crashes? b) Find the equation of the regression line between Full-Front and Full-rear crashes. c) What proportion of repair costs from full-front crashes can be explained by the costs of repair from full-rear crashes?
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.
Listed below are repair costs (in dollars) for cars crashed at 6mi/h in full-front crash tests and the same cars crashed at 6mi/h in full-rear crash tests (based on data from the Insurance Institute for Highway Safety). The cars are Toyota Camry, Mazda 6, Volvo S40, Saturn Aura, Subaru Legacy, Hyundai Sonata, and Honda Accord.
Front 936 978 2252 1032 3911 4312 3469
Rear 1480 1202 802 3191 1122 739 2767
a) Is there sufficient evidence to conclude that there is a
b) Find the equation of the regression line between Full-Front and Full-rear crashes.
c) What proportion of repair costs from full-front crashes can be explained by the costs of repair from full-rear crashes?
d) Find the best predicted repair costs for a full-rear crash for a Volkswagen Passat, given that its repair cost from a full-front crash is $4594. How does the result compare to the $982 actual repair cost from a full-rear crash?
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