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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

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