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Q54Section C (Section C)54 of 60

Least squares prediction from sums of squares and products

Based on 2020 observations (x1,y1),…,(x20,y20)(x_1,y_1),…,(x_{20},y_{20}), the following values are obtained: ∑i=120xi=6\sum_{i=1}^{20}x_i=6, ∑i=120xi2=14\sum_{i=1}^{20}x_i^2=14, ∑i=120yi=9\sum_{i=1}^{20}y_i=9 and ∑i=120xiyi=20\sum_{i=1}^{20}x_iy_i=20. For X=1X=1, the predicted value of YY based on a least squares fit of a linear regression model of YY on XX is ___________.

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