A statistics student is asked to estimate y = β₀ + β₁x + ε. She calculates the following values: = 440, = −568, , = 1,120, n = 11. Which of the following is the value of y if x equals 2?

Question

Quizplus · Accepted Answer

The given equation can be written as y = βS1U1B0(S1U1B10 + βS1U1B11x) + ε

We are given the values of S1U1B10, S1U1B11, and n. We need to calculate βS1U1B0.

Using the given values, we can calculate the regression coefficient for x as:

β = [(nΣXY) - (ΣX)(ΣY)] / [(nΣX^2) - (ΣX)^2)] = [(11 * 1120) - (2 * 440) - (11 * (-568))] / [(11 * (2^2)) - (2^2)] = 278 / 38 = 7.3158

Now, we need to calculate βS1U1B0:

βS1U1B0 = (11ea8309_a952_0402_b223_a912457f1b16_TB6618_11) / (nΣ(Xi - X)^2) = (11ea8309_a952_0402_b223_a912457f1b16_TB6618_11) / (11 * [(2 - 1.5455)^2 + (3 - 1.5455)^2 + ... +(12 - 1.5455)^2]) = 226.8889

Now, we can plug in the given values to get the value of y when x = 2:

y = (226.8889) * (S1U1B10 + 7.3158 * S1U1B11 * 2) + ε = (226.8889) * (1 + 7.3158 * 1 * 2) + ε = 58.22.

Therefore, the answer is C.

A Statistics Student Is Asked to Estimate Y = β0

A Statistics Student Is Asked to Estimate Y = β₀