Predictor variables in equation R2 Cp 0.015 0.000 100.1 х2 0.045 0.025 95.7 хз 0.098 0.079 87.8 X4 0.027 0.007 98.3 X1, X2 0.048 0.008 97.2 X1, X3 0.399 0.374 45.1 X1, X4 0.028 0.000 100.2 X2, X3 0.601 0.584 15.2 х2, X4 0.045 0.005 97.6 0.461 0.438 0.661 хз, х4 36.0 X], х2. хз 0.681 5.3 X1, X2, X4 0.049 0.000 99.1 0.518 0.486 0.638 X1, X3, X4 29.5 х2, х3. х4 0.660 8.4 X1, X2, X3, X4 0.697 0.670 5.0
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.
Suppose that x1, x2, x3, and x4 are predictor variables for a response variable y. The following table gives the value of R2, R2a and Cp for regression equations that involve each predictor variable individually, each pair of predictor variables, each triple of predictor variables, and all four predictor variables.
Employ the table to do the following.
a. Use the maximum-R2 criterion to obtain a regression equation for these data.
b. Use the adjusted-R2 criterion to obtain a regression equation for these data.
c. Use the Mallows’ Cp criterion to obtain a regression equation for these data.
d. Are the regression equations obtained in parts (a), (b), and (c) the same?
![Predictor variables
in equation
R2
Cp
0.015
0.000
100.1
х2
0.045
0.025
95.7
хз
0.098
0.079
87.8
X4
0.027
0.007
98.3
X1, X2
0.048
0.008
97.2
X1, X3
0.399
0.374
45.1
X1, X4
0.028
0.000
100.2
X2, X3
0.601
0.584
15.2
х2, X4
0.045
0.005
97.6
0.461
0.438
0.661
хз, х4
36.0
X], х2. хз
0.681
5.3
X1, X2, X4
0.049
0.000
99.1
0.518
0.486
0.638
X1, X3, X4
29.5
х2, х3. х4
0.660
8.4
X1, X2, X3, X4
0.697
0.670
5.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85ae81ef-d438-4d97-af22-efb8edc6b9f5%2Fb0933c9f-398c-4b52-90d3-5e80e6c70fc8%2F78uolwu.png&w=3840&q=75)
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