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Questions › IIT JAM › IIT JAM 2026 › Q60
2 marksEconometrics › Linear regression and OLS › The regression model and the OLS estimatorHardabout 3 min

IIT JAM 2026 Question 60: Linear regression and OLS

Consider the population regression Yi=α+βXi+uiY_i=\alpha+\beta X_i+u_iYi​=α+βXi​+ui​, estimated by OLS. Given sample size 100, ∑Xi2=460000\sum X_i^2=460000∑Xi2​=460000, ∑Yi2=320000\sum Y_i^2=320000∑Yi2​=320000, ∑Xi=6000\sum X_i=6000∑Xi​=6000, ∑Yi=500\sum Y_i=500∑Yi​=500, and ∑XiYi=40000\sum X_i Y_i=40000∑Xi​Yi​=40000. Then the estimated value of α\alphaα is ________ (in integer).

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Plain-text version

Consider the population regression Yᵢ=α+β Xᵢ+uᵢ, estimated by OLS. Given sample size 100, Σ Xᵢ²=460000, Σ Yᵢ²=320000, Σ Xᵢ=6000, Σ Yᵢ=500, and Σ Xᵢ Yᵢ=40000. Then the estimated value of α is (*in integer*).

Also written as: Consider the population regression Y_i=alpha+beta X_i+u_i, estimated by OLS. Given sample size 100, sum X_i^2=460000, sum Y_i^2=320000, sum X_i=6000, sum Y_i=500, and sum X_i Y_i=40000. Then the estimated value of alpha is (*in integer*).

Linear regression and OLS has come up 74 times in 7 exams since 2008.

What this question tests

This question is on The regression model and the OLS estimator, part of Linear regression and OLS in Econometrics.

What a linear regression model is and how ordinary least squares picks the fitted line.

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