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Q40Section B (Section B)40 of 60

Regression lines and correlation properties

Based on 1010 data points (x1,y1),(x2,y2),…,(x10,y10)(x_1, y_1), (x_2, y_2), \dots, (x_{10}, y_{10}) on a variable (X,Y)(X, Y), the simple regression lines of YY on XX and XX on YY are obtained as 2y−x=82y-x=8 and y−x=−3y-x=-3, respectively. Let xˉ=110∑i=110xi\bar{x}=\frac{1}{10}\sum_{i=1}^{10} x_i and yˉ=110∑i=110yi\bar{y}=\frac{1}{10}\sum_{i=1}^{10} y_i. Then, which of the following statements is/are TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.