Question

Use the following linear regression equation to answer the questions. X1 = 1.7 + 3.6x2 - 8.4x3 + 1.5x4 (a) Which variable is the response variable? O X1 O X2 O X4 O X3 Which variables are the explanatory variables? (Select all that apply.) X3 X1 U X2 (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 = 8, X3 = 5, and x4 = 4, what is the predicted value for X ? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." If we look at all coefficients together, each one can be thought of as a "slope." 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 xı? Suppose x2 increased by 2 units. What would be the expected change in X1?

Answer 1

Question (a)

The response variable is the dependent variable is usually on the left hand side of the equation

Response variable here is x₁

So Asnwer is Option A

The explanatory variables are the independent variables that are on the right side of the equation

Here the explanatory variables are x₂ , x₃ and x₄

Answers are Option A,B and D

Question (b)

Constant term = 1.7

x₂ coefficient = 3.6

x₃ coefficient = -8.4

x₄ coefficient = 1.5

Question (c)

Given x₂ = 8, x₃ = 5, x₄ = 4

The regression equation is

x₁ = 1.7 + 3.6 * x₂ - 8.4 * x₃ + 1.5 * x₄

x₁ = 1.7 + 3.6 * 8 - 8.4 * 5 + 1.5 * 4

x₁ = 1.7 + 28.8 - 42 + 6

x₁ = -5.5

Question (d)

If we hold all other explanatory variables or independent variables constant, then we can look at one coefficient as a slope

So Answer is Option D

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