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?

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(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
Transcribed Image Text:(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?
Transcribed Image Text: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 yi=β1+β2xi+ei

II yi=β1+γ1ri+β2xi+γ1xi ri+e¯i

where ri=1   if i corresponds to a rural area0                   Otherwise

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