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.

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Definitions:

Conjugate Acid

A chemical species formed by the reception of a proton (H+) by a base, often involved in acid-base reactions.

Hydrogen Bonds

Weak bonds between a hydrogen atom in one molecule and an electronegative atom in another, crucial for the structure of many biological molecules.

Nonpolar Covalent

Nonpolar Covalent bonds are chemical bonds where two atoms share a pair of electrons equally, resulting in molecules that have no overall dipole moment.