Does prison really deter violent crime? Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained. x 5.7 5.3 4.3 5.2 6.2 6.5 11.1 y −1.8 −4.3 −8.0 −4.0 3.6 −0.1 −4.4 Complete parts (a) through (e), given Σx = 44.3, Σy = −19, Σx2 = 310.01, Σy2 = 134.06, Σxy = −115.42, and r ≈ 0.098. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x
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.
Does prison really deter violent crime? Let x represent percent change in the rate of violent crime and y represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained.
| x | 5.7 | 5.3 | 4.3 | 5.2 | 6.2 | 6.5 | 11.1 |
| y |
−1.8
|
−4.3
|
−8.0
|
−4.0
|
3.6 |
−0.1
|
−4.4
|
Complete parts (a) through (e), given Σx = 44.3,
Σx2 = 310.01, Σy2 = 134.06,
and r ≈ 0.098.
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample
| Σx = | |
| Σy = | |
| Σx2 = | |
| Σy2 = | |
| Σxy = | |
| r = |
(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
| x | = | |
| y | = | |
| = | + x |
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