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:

Firm-specific Events

Events that directly affect a company's operations, financial performance, or stock price, independent of the market or economic conditions.

Macroeconomic Events

Large-scale economic events that affect the economy on a national or global level, such as inflation, unemployment, or fiscal policies.

Unsystematic Risk

The segment of risk that is unique to a specific company or industry, also known as diversifiable risk, which can be mitigated through diversification.

Diversification

Spreading a portfolio over many investments to avoid excessive exposure to any one source of risk.