(8SE SSF)/2is larger than the critical value for F(2,21) distribution, we reject the hypothesis that the coefficients for rut and urtun areasequalO,SSE-SSEF)/2SSK1/21is larger that the critical value for the F(2,21) distribution, we reject the hypothesis that the coefficients for runal and surtun arequalO (SSE-8SE)/2SSE/15is larger that the critical value for the F(2.15) distribution, we reject the hypothesis that the coefficients for rural and urban aaequalO Since r is a linear combination of the other explanatory varnables the coeffcient of r, cannot be estimated by OLS(SSE-SSE}/2SSE/10is larger that the critical value for the Fa10) distribution we reject the hypothesis that the coefficients for rural and urbun ar areitequal A researcher wants to analyze the effect of a variable x on another variable y using observations from both rural and urban areas. Heobtained 15 observations from rural areas, 10 observations from urban areas, and estimated the model(1) w=B +Baa, + eTo consider the possibility that the coefficients are different for the two types of observations, the researcher also estimated the model(II) B +nn+BI +2 (z, r,) + ë,whereif i corresponds to a rural area0 otherwiseDenote the sum of squared residuals from the OLS regressions of (I) and (II) by, respectively SSE, and SSE1-Which of the following statements is true?

A researcher wants to analyze the effect of a variable x on another variable y using observations from both rural and urban areas He obtained 15 observations from rural areas, 10 observations from urban areas, and estimated the model (1) w-B +B, + e To consider the possibility that the coefficients are different for the two types of observations, the researcher also estimated the model (II) -8+nn + Bz I, + 72 (z, r.) + č, where |i ifi corresponds to a rural area O otherwise Denote the sum of squared residuals from the OLS regressions of (1) and (II) by, respectively SSE, and SSE1- Which of the following statements is true?

A researcher wants to analyze the effect of a variable x on another variable y using observations from both rural and urban areas He obtained 15 observations from rural areas, 10 observations from urban areas, and estimated the model (1) w-B +B, + e To consider the possibility that the coefficients are different for the two types of observations, the researcher also estimated the model (II) -8+nn + Bz I, + 72 (z, r.) + č, where |i ifi corresponds to a rural area O otherwise Denote the sum of squared residuals from the OLS regressions of (1) and (II) by, respectively SSE, and SSE1- Which of the following statements is true?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

(8SE SSF)/2
is larger than the critical value for F(2,21) distribution, we reject the hypothesis that the coefficients for rut and urtun areas
equal
O,SSE-SSEF)/2
SSK1/21
is larger that the critical value for the F(2,21) distribution, we reject the hypothesis that the coefficients for runal and surtun ar
equal
O (SSE-8SE)/2
SSE/15
is larger that the critical value for the F(2.15) distribution, we reject the hypothesis that the coefficients for rural and urban aa
equal
O Since r is a linear combination of the other explanatory varnables the coeffcient of r, cannot be estimated by OLS
(SSE-SSE}/2
SSE/10
is larger that the critical value for the Fa10) distribution we reject the hypothesis that the coefficients for rural and urbun ar are
it
equal

A researcher wants to analyze the effect of a variable x on another variable y using observations from both rural and urban areas. He
obtained 15 observations from rural areas, 10 observations from urban areas, and estimated the model
(1) w=B +Baa, + e
To consider the possibility that the coefficients are different for the two types of observations, the researcher also estimated the model
(II) B +nn+BI +2 (z, r,) + ë,
where
if i corresponds to a rural area
0 otherwise
Denote the sum of squared residuals from the OLS regressions of (I) and (II) by, respectively SSE, and SSE1-
Which of the following statements is true?

Expert Solution

Step 1

Given the estimated model for the variables x and y as

$(I) y_{i} = β_{1} + β_{2} x_{i} + e_{i}$

$(I I) y_{i} = β_{1} + γ_{1} r_{i} + β_{2} x_{i} + γ_{1} (x_{i} r_{i}) + {\bar{e}}_{i}$

where $r_{i} = \{\begin{cases} 1 i f i c o r r e s p o n d s t o a r u r a l a r e a \\ 0 O t h e r w i s e \end{cases}$

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