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:

Indwelling Urinary Catheter

A tube inserted into the bladder to allow continuous urine drainage, used for patients who cannot void naturally.

Difficulty Voiding

Describes a condition where an individual experiences trouble starting or maintaining urine flow.

Hourly Urine Output

The volume of urine produced and expelled by the kidneys and bladder over the span of an hour, an important indicator of kidney health and fluid balance.

Catheter With Sterile Solution

A medical device, often a tube, used to deliver or remove fluids from the body, which is used with a sterile solution to prevent infection.