Multiple Regression Analysis Was Used to Study How an Individual's

question 11

Essay

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 individual'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. $\begin{array}{ll}&\text { Coefficients } & \text { Standard Error } \\x _ { 1 } &0.625 & 0.094 \\x _ { 2 } &0.921 & 0.190 \\x _ { 3 } &-0.510 & 0.920\end{array}$
ANOVA
$\begin{array}{llll} & d f & S S & M S&F \\\text { Regression } && 84 &\\\text { Error } &&112 &\end{array}$ ​
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 = .05, 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.