A Student Used Multiple Regression Analysis to Study How Family

question 29

Essay

A student used multiple regression analysis to study how family spending (y) is influenced by income (x₁), family size (x₂), and additions to savings (x₃). The variables y, x₁, and x₃ are measured in thousands of dollars. The following results were obtained.
Coefficient of determination = 0.946
a.Write out the estimated regression equation for the relationship between the variables.
b.What can you say about the strength of this relationship?
c.Carry out a test of whether y is significantly related to the independent variables. Use a .05 level of significance.
d.Carry out a test to see if x₃ and y are significantly related. Use a .05 level of significance.
e.Why would a coefficient of determination very close to 1.0 be expected here?

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Definitions:

Operational Decision

An Operational Decision involves choices made by an organization's management regarding day-to-day operations that affect its performance and efficiency.

Primary Market

The financial market segment where new securities are issued and sold for the first time, often through public offerings or private placements.

Securities

Ownership instruments in the form of stocks for publicly-quoted companies, creditor agreements represented by bonds with either corporations or governmental bodies, or claims to ownership through options.

General Public

The broad group of people in society who do not have a specialized interest in financial markets or investments but may be affected by its outcomes.