Question

Use the following linear regression equation to answer the questions.

x₁ = 1.4 + 3.1x₂ – 8.2x₃ + 2.1x₄

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 = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.461. Construct a 95% 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 ±

Answer 1

Answer: The given Equation is Xi = 1.44 3.1724273+2-124 Obtain the Constant term and obtain the table. Constant 1.47 3.1 X-Coefficient -8.2 Xz-Coefficient 2.1 X4 - Coefficient - If x2 in x is increased by 1 unit, then the Corresponding Change X = 14 +31(1)-8-233 +2:124 E6%) = 14.5-8.2 33+2.134 If x2 increased by 2 units, then the corresponding Change in x, is X, -14 +3.1(2)-8.2 X3 +2.124 (C)) = 7.6-8.223 +2.1.X4 If X2 is increased by 4 Units, then the corresponding Change in x B X, =) 4+31(4)-8.243+21 X4 2, 113.8 - 8243 +2:124 Given n=13 Standard error of the Coefficient f = 0.461 Confidence intewel i 95%.

(2 LE I-CI = 1-0.95 -0.05 df = n-4-13-4-9 Gitical value of t to.o5 씰 to.025 A *2.571 - 95% Confidence interval is, C.I B2 + tapy Se (B) * Keeping the stariable X3,264 fisced a Unit increases the variable x, increases by 3.1 Units. in the 22, C. I. 3.1 + 2.571 * 0.461 3.1 1.185 Lower Limit = 3.1-1-185 = 1.915 Upper Limit = 3.1 + 1.185= 4.285 Test Statistic: test. Stastistic Sielka) -6.72 0.461 t = 6-721 Level of Significance = 1% = 0.0), df = 9 3.1 Critical value of t 42. - = 3.250 0