A Student Used Multiple Regression Analysis to Study How Family

question 36

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.
ANOVA
DF SS
Regression 3 45.9634
Residual 11 2.6218 Total
$\begin{array}{lr}&\text { Coefilicient }&\text { Standard Error }\\\text { Intercept } & 0.0136 \\\mathrm{X}_{1} & 0.7992&0.074 \\\mathrm{X}_{2} & 0.2280&0.190 \\\mathrm{X}_{3} & -0.5796&0.920\end{array}$
a. Write out the estimated regression equation for the relationship between the variables.
b. Compute R². 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.

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Definitions:

Equity Method

An accounting technique used to record investments in associate companies, where the investment is initially recognized at cost and subsequently adjusted for the investor’s share of the investee’s profit or loss.

Investment Account

A financial account held at a brokerage or financial institution that contains securities, cash, and other holdings for investment purposes.

Common Shares

Equity securities that represent ownership in a corporation, providing voting rights and entitling holders to a share of the company's profits via dividends.

Dividend

A share of profits distributed by a company to its shareholders, typically in the form of cash or additional stock.