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A Student Used Multiple Regression Analysis to Study How Family

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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.
A student used multiple regression analysis to study how family spending (y) is influenced by income (x<sub>1</sub>), family size (x<sub>2</sub>), and additions to savings (x<sub>3</sub>). The variables y, x<sub>1</sub>, and x<sub>3</sub> 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 x<sub>3</sub> 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? 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?


Definitions:

Artifact Theory

A perspective suggesting that observed differences in certain measures across cultures or groups are not due to actual differences in the constructs being measured, but due to the measurement instruments or procedures.

Developmental Psychopathology

The study of how psychological disorders arise and change with time, often emphasizing how childhood experiences can influence adulthood.

Depression

A common mental disorder marked by persistent sadness, loss of interest in activities, and decreased energy.

Divorce

The legal dissolution of a marriage by a court or other competent body, officially ending the legal relationship between the partners.

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