A sociologist is interested in the relation between ?, the number of job changes and ?, the annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information: X 4 7 5 6 1 5 9 10 10 3 Y 33 37 34 32 32 38 43 37 40 33 a) The regression equation is: _____ b) Graph the data and the regression equation on the same graph. Label the graph. c) Describe the apparent relationship between the number of job changes and annual salary. d) What does the slope of the regression equation represent in terms of the annual salary? e) Identify any outliers or potential influential observations. Explain your reasoning. f) Identify the predictor and response variables g)r^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 is interested in the relation between ?, the number of job changes and ?, the annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information:
| X | 4 | 7 | 5 | 6 | 1 | 5 | 9 | 10 | 10 | 3 |
| Y | 33 | 37 | 34 | 32 | 32 | 38 | 43 | 37 | 40 | 33 |
a) The regression equation is: _____
b) Graph the data and the regression equation on the same graph. Label the graph.
c) Describe the apparent relationship between the number of job changes and annual salary.
d) What does the slope of the regression equation represent in terms of the annual salary?
e) Identify any outliers or potential influential observations. Explain your reasoning.
f) Identify the predictor and response variables
g)r^2=_____
h)r=_____
i) Interpret the meaning of r2 and how useful the regression equation is for making predictions.
j) Interpret the meaning of r in terms of the linear relationship between the number of job changes and annual salary.
k) Use the regression equation to predict the annual salary of a randomly selected employee who has had 8 job changes.
l) A particular employee who has had 8 job changes has an annual salary of $35,000. Calculate the residual for this data employee, to the nearest cent.
m) Give a short interpretation of the y-intercept of the regression line in the context of the problem.
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