Enrollment (thousands) 53 28 27 36 42 Burglaries 86 57 32 131 157 For the following problems, use the sample data in the table above consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges. Enrollment (thousands) 53 28 27 36 42 Burglaries 86 57 32 131 157 1. Find the linear correlation coefficient r and the critical values for a 0.05 significance level. What can be determined from this? 2. Which of the following change if the two variables of enrollment and burglaries are switched: the value of r, the critical values? 3. Does the value of r change from what was found in question 1 if the actual enrollment numbers of 53,000, 28,000, 27,000, 36,000 and 42,000 are used instead of 53, 28, 27, 36 and 42? 4. If you had calculated the value of the linear correlation coefficient to be 1.247, what should you conclude? 5. Find the regression equation for the sample data. What is the best-predicted number of burglaries, given an enrollment of 50 (thousand) and how did you find it? 6. Repeat the previous question, assuming that the linear correlation coefficient is r = 0.997. 7. Using the original linear correlation coefficient r that you found in question 1, what is the proportion of the variation in numbers of burglaries that is explained bu the linear relationship between enrollment and the number of burglaries? 8. True or false: If there is no linear correlation between enrollment and the number of burglaries, then those two variables are not related in any way.
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.
Enrollment (thousands) 53 28 27 36 42 Burglaries 86 57 32 131 157
For the following problems, use the sample data in the table above consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges.
| Enrollment (thousands) | 53 | 28 | 27 | 36 | 42 |
| Burglaries | 86 | 57 | 32 | 131 | 157 |
1. Find the linear
2. Which of the following change if the two variables of enrollment and burglaries are switched: the value of r, the critical values?
3. Does the value of r change from what was found in question 1 if the actual enrollment numbers of 53,000, 28,000, 27,000, 36,000 and 42,000 are used instead of 53, 28, 27, 36 and 42?
4. If you had calculated the value of the linear correlation coefficient to be 1.247, what should you conclude?
5. Find the regression equation for the sample data. What is the best-predicted number of burglaries, given an enrollment of 50 (thousand) and how did you find it?
6. Repeat the previous question, assuming that the linear correlation coefficient is r = 0.997.
7. Using the original linear correlation coefficient r that you found in question 1, what is the proportion of the variation in numbers of burglaries that is explained bu the linear relationship between enrollment and the number of burglaries?
8. True or false: If there is no linear correlation between enrollment and the number of burglaries, then those two variables are not related in any way.
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