Distance to Work Number of (miles) Days Absent 1 8 3 5 4 8 6. 7 10 3 12 14 14 18 2
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.
A sociologist was hired by a large city hospital to investigate the relationship between the
number of unauthorized days that employees are absent per year and the distance (miles)
between home and work for the employees. A sample of 10 employees was chosen, and
the following data were collected.
a. Develop a scatter chart for these data. Does a linear relationship appear reasonable?
Explain.
b. Use the data to develop an estimated regression equation that could be used to predict the
number of days absent given the distance to work. What is the estimated regression model?
c. What is the 99 percent confidence interval for the regression parameter b1? Based on
this interval, what conclusion can you make about the hypotheses that the regression
parameter b1 is equal to zero?
d. What is the 99 percent confidence interval for the regression parameter b0? Based on
this interval, what conclusion can you make about the hypotheses that the regression
parameter b0 is equal to zero?
e. How much of the variation in the sample values of number of days absent does the
model you estimated in part b explain?
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