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Use the following linear regression equation to answer the questions. X - 1.2 + 3.6x - 7.6xy + 2.5x4 (a) Which variable is the response variable? O KA O x2 Oxy Which variables are the explanatory variables? (Select all that apply.) (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 12 X2 coefficient 3.6 Xy coefficient 7.6 X4 coefficient 2.5 (c) If x - 8, x - 6, and x4 - 4, what is the predicted value for x? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope."

Use the following linear regression equation to answer the questions. X - 1.2 + 3.6x - 7.6xy + 2.5x4 (a) Which variable is the response variable? O KA O x2 Oxy Which variables are the explanatory variables? (Select all that apply.) (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 12 X2 coefficient 3.6 Xy coefficient 7.6 X4 coefficient 2.5 (c) If x - 8, x - 6, and x4 - 4, what is the predicted value for x? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope."

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 60E
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Use the following linear regression equation to answer the questions. X1 = 1.2 + 3.6x2 - 7.6x3 + 2.5x4 (a) Which variable is the response variable? X1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 | 4 V x2 V x3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 1.2 X2 coefficient|3.6 X3 coefficient 7.6 Xa coefficient 2.5 (c) If x2 = 8, X3 = 6, and x4 = 4, what is the predicted value for x,? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. O 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 x,? 3.6 Suppose x2 increased by 2 units. What would be the expected change in X1? 7.2 Suppose x2 decreased by 4 units. What would be the expected change in x1? 14.4
Transcribed Image Text:Use the following linear regression equation to answer the questions. X1 = 1.2 + 3.6x2 - 7.6x3 + 2.5x4 (a) Which variable is the response variable? X1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 | 4 V x2 V x3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant 1.2 X2 coefficient|3.6 X3 coefficient 7.6 Xa coefficient 2.5 (c) If x2 = 8, X3 = 6, and x4 = 4, what is the predicted value for x,? (Use 1 decimal place.) 5.6 (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. O 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 x,? 3.6 Suppose x2 increased by 2 units. What would be the expected change in X1? 7.2 Suppose x2 decreased by 4 units. What would be the expected change in x1? 14.4
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