Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.6x2 – 7.8x3 + 1.8x4 (a) Which variable is the response variable? answer: x1 Which variables are the explanatory variables? (Select all that apply.) answer: x4x3x2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 1.5 x2 coefficient 3.6 x3 coefficient -7.8 x4 coefficient 1.8 (c) If x2 = 10, x3 = 7, and x4 = 7, what is the predicted value for x1? (Use 1 decimal place.) answer: -4.5 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. answer: If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." 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? answer: 3.6 Suppose x2 increased by 2 units. What would be the expected change in x1? answer: 7.2 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 7.81 t critical ±

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.3: Lines

Problem 92E

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Concept explainers

Question

Use the following linear regression equation to answer the questions.

x₁ = 1.5 + 3.6x₂ – 7.8x₃ + 1.8x₄

(a) Which variable is the response variable?

answer: x₁

Which variables are the explanatory variables? (Select all that apply.)

answer: x₄x₃x₂

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

constant	1.5
x₂ coefficient	3.6
x₃ coefficient	-7.8
x₄ coefficient	1.8

answer: -4.5

(d) Explain how each coefficient can be thought of as a "slope" under certain conditions.

answer: If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."

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?

answer: 3.6

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

answer: 7.2

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	7.81
t critical ±

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