The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following questions. Dependent Variable: Y Method: Least Squares Date: 12/28/16 Time: 15:29 Sample: 2000 2010 Included observations: 11 Variable Coefficient Std. Error t-Statistic Prob. C 0.229334 2.938536 0.078044 0.9395 X 0.354833 0.024783 14.31783 0.0000 R-squared 0.957944 Mean dependent var 37.45455 Adjusted R-squared 0.953271 S.D. dependent var 21.01125 S.E. of regression 4.541976 Akaike info criterion 6.027567 Sum squared resid 185.6659 Schwarz criterion 6.099911 Log likelihood -31.15162 Hannan-Quinn criter. 5.981964 F-statistic 205.0003 Durbin-Watson stat 1.111860 Prob(F-statistic) 0.000000 a) Write the regressed equation and interpret the slope and the intercept. b) Construct a confidence interval for the slope (b2) at 95% confidence level. c) Test whether the slope is equal or not equal to zero at 95% confidence level.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the output table below, answer the following questions.

Dependent Variable: Y
Method: Least Squares
Date: 12/28/16 Time: 15:29
Sample: 2000 2010
Included observations: 11


Variable	Coefficient	Std. Error	t-Statistic	Prob.


C	0.229334	2.938536	0.078044	0.9395
X	0.354833	0.024783	14.31783	0.0000


R-squared	0.957944	Mean dependent var	37.45455
Adjusted R-squared	0.953271	S.D. dependent var	21.01125
S.E. of regression	4.541976	Akaike info criterion	6.027567
Sum squared resid	185.6659	Schwarz criterion	6.099911
Log likelihood	-31.15162	Hannan-Quinn criter.	5.981964
F-statistic	205.0003	Durbin-Watson stat	1.111860
Prob(F-statistic)	0.000000

a) Write the regressed equation and interpret the slope and the intercept.

b) Construct a confidence interval for the slope (b₂) at 95% confidence level.

c) Test whether the slope is equal or not equal to zero at 95% confidence level.

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