Weekly Usage (hours) Annual Maintenance Expense ($100s) 13 17.0 22.0 30.0 37.0 10 20 28 32 47.0 17 30.5 24 32.5 31 39.0 40 51.5 38 40.0
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.
Jensen Tire & Auto is deciding whether to purchase a maintenance contract for its new
computer wheel alignment and balancing machine. Managers feel that maintenance expense
should be related to usage, and they collected the following information on weekly
usage (hours) and annual maintenance expense (in hundreds of dollars).
a. Develop a scatter chart with weekly usage hours as the independent variable. What
does the scatter chart indicate about the relationship between weekly usage and annual
maintenance expense?
b. Use the data to develop an estimated regression equation that could be used to predict
the annual maintenance expense for a given number of hours of weekly usage. 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 expense does
the model you estimated in part b explain?
e. If the maintenance contract costs $3,000 per year, would you recommend purchasing
it? Why or why not?
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