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Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let b1 and b2 be the estimators for B1 and ß2 and recall ở = 5Eế, where ê; = Y; – bị – b2X¡. Suppose the sample correlation between {X¡ }"-1 and {Y;}"_, is 0.5 and E-(Y; – Ý „)² = 100. What is ở? n-2

Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let b1 and b2 be the estimators for B1 and ß2 and recall ở = 5Eế, where ê; = Y; – bị – b2X¡. Suppose the sample correlation between {X¡ }"-1 and {Y;}"_, is 0.5 and E-(Y; – Ý „)² = 100. What is ở? n-2

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let bj and b2 be the estimators for B1 and B2 and recall Eê, where ê; = Y; – bị – b2X;. Suppose the sample correlation between {X; }"_-1 and {Y;}"_, is 0.5 and E(Y; – Ỹ„)² = 100. What is ổ?? %3D n-2 Hint: (i) for simple regression, the regression R? is equal to the squared sample correlation between X and Y. (ii) R² = 1 – SSE where SSE = Eế and SST SST = O a. 7.5 O b. 8.5 О с. 9 O d. 10 O e. 8 O f. 7 Clear my choice
Transcribed Image Text:Consider the model Y = B1 + B2X + e, which we estimate using a random sample with 12 observations. Let bj and b2 be the estimators for B1 and B2 and recall Eê, where ê; = Y; – bị – b2X;. Suppose the sample correlation between {X; }"_-1 and {Y;}"_, is 0.5 and E(Y; – Ỹ„)² = 100. What is ổ?? %3D n-2 Hint: (i) for simple regression, the regression R? is equal to the squared sample correlation between X and Y. (ii) R² = 1 – SSE where SSE = Eế and SST SST = O a. 7.5 O b. 8.5 О с. 9 O d. 10 O e. 8 O f. 7 Clear my choice
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