MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A sample of 23 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.
Intercept
ŷ =
X1
X2
X3
ANOVA
Coefficients
Regression
Residual (Error)
474.31
51.94
13.72
-1.12
df
Standard Error
SS
1,852.50
(a) Write out the estimated regression equation.
56.6
9.8
2.8
16.0
3,188.25 1,062.75
MS
97.50
474.31 +51.94x₁ + 13.72x2 -1.12x3
J
(b) Interpret all coefficients.
An additional member in the family increases the monthly expenditure in dollars on average by $
expenditure on food in dollars on average by $
on a diet.
holding all other variables constant. An additional meal eaten outside increases the monthly
if a family member is
, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $
(c) Test for the significance of ß, at the 1% level of significance.
State the null and alternative hypotheses. (Enter != for as needed.)
Ho:
#
hp
2:10 PM
12/2/2022
Transcribed Image Text:You may need to use the appropriate technology to answer this question.
A sample of 23 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.
Intercept
ŷ =
X1
X2
X3
ANOVA
Coefficients
Regression
Residual (Error)
474.31
51.94
13.72
-1.12
df
Standard Error
SS
1,852.50
(a) Write out the estimated regression equation.
56.6
9.8
2.8
16.0
3,188.25 1,062.75
MS
97.50
474.31 +51.94x₁ + 13.72x2 -1.12x3
J
(b) Interpret all coefficients.
An additional member in the family increases the monthly expenditure in dollars on average by $
expenditure on food in dollars on average by $
on a diet.
holding all other variables constant. An additional meal eaten outside increases the monthly
if a family member is
, holding all other variables constant. The monthly food expenditures in dollars decrease on average by $
(c) Test for the significance of ß, at the 1% level of significance.
State the null and alternative hypotheses. (Enter != for as needed.)
Ho:
#
hp
2:10 PM
12/2/2022
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