Question

Use the following linear regression equation to answer the questions.

x₁ = 1.7 + 3.6x₂ – 7.7x₃ + 2.4x₄

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

constant
x2 coefficient
x3 coefficient
x4 coefficient

If x₂ = 1, x₃ = 8, and x₄ = 9, what is the predicted value for x₁? (Use 1 decimal place.)

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 = 11 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.363. Construct a 99% 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 5%, test the claim that the coefficient of x₂ is different from zero. (Use 2 decimal places.)

t
t critical ±

Answer 1

constant	1.7
x2 coefficient	3.6
x3 coefficient	-7.7
x4 coefficient	2.4

x₁ = 1.7 + 3.6x₂ – 7.7x₃ + 2.4x₄

_{= 1.7 + 3.6 - 7.7 *8 + 2.4 *9}

₌ -34.7

x₂ increased by 1 unit. What would be the corresponding change in x₁?

increase by 3.6


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

increase by 3.6*2 = 7.2


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

decrease by 3.6 *4 = 14.4

e)

df = n-k -1 = 11 - 3-1 = 7

for 99 % confidence interval

t = 3.5

(3.6 - 3.5* 0.363 , 3.6 + 3.5 * 0.363)

=(2.3295 , 4.8705)

f) t = (3.6 - 0)/0.363 = 9.917

critical value = 2.365

9.917 > 2.365

we reject the null