5. Multiple regression analysis was used to
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5. Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 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.
|
| Coefficient | Standard Error |
|
|
| X1 | 0.6251 | 0.094 |
|
|
| X2 | 0.9210 | 0.190 |
|
|
| X3
| -0.510 | 0.920 |
|
|
| Analysis of Variance
|
|
|
|
|
| Source of Variation | Degrees of Freedom | Sum of Squares | Mean Square | F |
| Regression |
| 84 |
|
|
| Error |
| 112 |
|
|
| a. | Compute the coefficient of determination. (10%) |
| 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 |
| c. | At |
| d. | As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient. (5%) |
. (10%)
