Multiple regression analysis was used to study how an individual's income ( y in thousands of dollars) is influenced by age ( x 1 in years), level of education ( x 2 ranging from 1 to 5), and the individual's gender ( x 3 where 0 = female and 1 = male). The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficients Standard Error x1 0.625 0.094 x2 0.921 0.190 x3 -0.510 0.920 ANOVA df SS MS F Regression 84 Error 112 a. Compute the multiple coefficient of determination. b. Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., x2) is significantly different from zero. Let α = .05. c. At α = .1, 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.
|
Coefficients |
Standard Error |
|||
| x1 |
0.625 |
0.094 |
||
| x2 |
0.921 |
0.190 |
||
| x3 |
-0.510 |
0.920 |
||
| ANOVA |
||||
|
df |
SS |
MS |
F |
|
| Regression |
84 |
|||
| Error |
112 |
| a. | Compute the multiple coefficient of determination. |
| b. | Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., x2) is significantly different from zero. Let α = .05. |
| c. | At α = .1, perform an F test and determine whether or not the regression model is significant. |
| d. | As you note, the coefficient of x3 is -.510. Fully interpret the meaning of this coefficient. |
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