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  . (10%)
|
| c.
| At , perform an F test and determine whether or not the regression model is significant. (5%)
|
| d.
| As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient. (5%)
|
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