The data points in ExerciseIn each of Exercises, we have presented two linear equations and a set of data points. For each exercise,a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.b. construct tables for x, y,ŷ e, and e2 like Table (page 626).c. determine which line fits the set of data points better, according to the least-squares criterion.TABLEDetermining how well the data points in Table are fit by (a) Line A and (b) Line Ba. Line A: y= -1 + 2x x y ŷ e e2 1 3 1 2 4 2 1 3 -2 4 3 5 5 0 0 8 b. Line B: y= -1 + x x y ŷ e e2 1 3 2 1 1 2 1 3 -2 4 3 5 4 1 1 6 TABLE Three data points x y 1 3 2 1 3 5 Line A: y=3-0.6x, Line B: y=4-xData Points x 0 2 2 5 6 y 4 2 0 -2 1 ŷ =1+2x x 1 2 3 y 4 3 8
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.
The data points in Exercise
In each of Exercises, we have presented two linear equations and a set of data points. For each exercise,
a. plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.
b. construct tables for x, y,ŷ e, and e2 like Table (page 626).
c. determine which line fits the set of data points better, according to the least-squares criterion.
TABLE
Determining how well the data points in Table are fit by (a) Line A and (b) Line B
a.
| Line A: y= -1 + 2x | ||||
| x | y | ŷ | e | e2 |
| 1 | 3 | 1 | 2 | 4 |
| 2 | 1 | 3 | -2 | 4 |
| 3 | 5 | 5 | 0 | 0 |
| 8 |
b.
| Line B: y= -1 + x | ||||
| x | y | ŷ | e | e2 |
| 1 | 3 | 2 | 1 | 1 |
| 2 | 1 | 3 | -2 | 4 |
| 3 | 5 | 4 | 1 | 1 |
| 6 |
TABLE Three data points
| x | y |
| 1 | 3 |
| 2 | 1 |
| 3 | 5 |
Line A: y=3-0.6x, Line B: y=4-x
Data Points
| x | 0 | 2 | 2 | 5 | 6 |
| y | 4 | 2 | 0 | -2 | 1 |
ŷ =1+2x
| x | 1 | 2 | 3 |
| y | 4 | 3 | 8 |
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