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Multiple regression analysis

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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
-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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