A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x1), the number of meals eaten outside (x2), and a dummy variable (x3) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained. Coefficients Standard Error Intercept 450.08 53.6 x1 49.92 9.6 x2 10.12 2.2 x3 -.60 12.0 ANOVA df SS MS Regression 3078.39 1026.13 Residual (Error) 2013.90 95.90 Total Write out the estimated regression equation. Interpret all coefficients. Test for the significance of β1, β2, and β3 at the 1% level of significance. What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? Test whether or not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a .01 level of significance. Be sure to state the null and alternative hypotheses. Compute the multiple coefficient of determination and explain its meaning. Estimate the monthly expenditure on food for a family that has 4 members, eats out 3 times, and does not have any member of the family on a diet.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Equations, Inequalities, And Mathematical Modeling

Section: Chapter Questions

Problem 22T: On the first part of a 350-kilometer trip, a salesperson travels 2 hours and 15 minutes at an...

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A sample of 25 families was taken for a study. The objective of the study was to estimate the factors that determine the monthly expenditure (in dollars) on food for families. The independent variables included in the analysis were the number of members in the family (x₁), the number of meals eaten outside (x₂), and a dummy variable (x₃) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following regression results were obtained.

	*Coefficients*	*Standard Error*
Intercept	450.08	53.6
x₁	49.92	9.6
x₂	10.12	2.2
x₃	-.60	12.0

ANOVA
	df	SS	MS
Regression		3078.39	1026.13
Residual (Error)		2013.90	95.90
Total

Write out the estimated regression equation.
Interpret all coefficients.
Test for the significance of β₁, β₂, and β₃ at the 1% level of significance.
What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)?
Test whether or not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a .01 level of significance. Be sure to state the null and alternative hypotheses.
Compute the multiple coefficient of determination and explain its meaning.
Estimate the monthly expenditure on food for a family that has 4 members, eats out 3 times, and does not have any member of the family on a diet.

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