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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

A Student Used Multiple Regression Analysis to Study How Family