Multiple regression analysis was used to study the relationship between a dependent variable, y, and four independent variables; x1, x2, x3, and x4. The following is a partial result of the regression analysis involving 31 observations. Coefficients Standard Error Intercept 18.00 6.00 x1 12.00 8.00 x2 24.00 48.00 x3 -36.00 36.00 x4 16.00 2.00 ANOVA df SS MS F Regression 125 Error Total 760 Compute the multiple coefficient of determination. Perform a t test and determine whether or not β1 is significantly different from zero (α = .05). Perform a t test and determine whether or not β4 is significantly different from zero (α = .05). At α = .05, perform an F test and determine whether or not the regression model is significant.
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.
- Multiple
regression analysis was used to study the relationship between a dependent variable, y, and four independent variables; x1, x2, x3, and x4. The following is a partial result of the regression analysis involving 31 observations.
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|
Coefficients |
Standard Error |
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|
|
Intercept |
18.00 |
6.00 |
|
|
|
x1 |
12.00 |
8.00 |
|
|
|
x2 |
24.00 |
48.00 |
|
|
|
x3 |
-36.00 |
36.00 |
|
|
|
x4 |
16.00 |
2.00 |
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|
|
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df |
SS |
MS |
F |
|
Regression |
|
|
125 |
|
|
Error |
|
|
|
|
|
Total |
|
760 |
|
|
- Compute the multiple coefficient of determination.
- Perform a t test and determine whether or not β1 is significantly different from zero (α = .05).
- Perform a t test and determine whether or not β4 is significantly different from zero (α = .05).
- At α = .05, perform an F test and determine whether or not the regression model is significant.
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