18 ) Use the following linear regression equation to answer the questions. x1 = 1.8 +...

18 ) Use the following linear regression equation to answer the questions.

x₁ = 1.8 + 3.1x₂ – 7.6x₃ + 1.5x₄

(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.

constant
x₂ coefficient
x₃ coefficient
x₄ coefficient

(c) If x₂ = 9, x₃ = 10, and x₄ = 5, what is the predicted value for x₁? (Use 1 decimal place.)

d) Suppose x₃ and x₄ were held at fixed but arbitrary values and x₂ increased by 1 unit. What would be the corresponding change in x₁?

Suppose x₂ increased by 2 units. What would be the expected change in x₁?

Suppose x₂ decreased by 4 units. What would be the expected change in x₁?

(e) Suppose that n = 9 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.335. Construct a 90% confidence interval for the coefficient of x₂. (Use 2 decimal places.)

lower limit
upper limit

(f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x₂ is different from zero. (Use 2 decimal places.)

t
t critical ±

Expert Solution

orchestra answered 1 year ago

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