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In: Statistics and Probability

For the cultivation of a cereal, an amount of fertilizer x is applied in Kgs, per...

For the cultivation of a cereal, an amount of fertilizer x is applied in Kgs, per unit area and the quantity y of tons of production is obtained. The following data is available:

x 99 100 101 102 103 104 105 106

y 2.1 2.8 7.2. 9.9 9.3 13.6 14.7 17.1

Do the test: H_0: β1 = 0 VS  H_1: β1 ≠ 0 . Use α = 0.005.

Make a confidence interval (α = 0.005) for β1.

What would be a prediction interval for future production if x_h = 101 is used? Use 1 − α = 1−0.005

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