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Use the following linear regression equation to answer the questions. X- 1.2+ 3.6x - 7.6x + 2.5x4 (a) Which variable is the response variable? O 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 2 coefficient Xy coefficient

Use the following linear regression equation to answer the questions. X- 1.2+ 3.6x - 7.6x + 2.5x4 (a) Which variable is the response variable? O 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 2 coefficient Xy coefficient

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter4: Linear Functions
Section4.3: Fitting Linear Models To Data
Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...
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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? O x1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 O X4 O X3 (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 = 6, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.) (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." 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 x, increased by 1 unit. What would be the corresponding change in x,? Suppose x2 increased by 2 units. What would be the expected change in x,? Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.321. Construct a 99% confidence interval for the coefficient of xɔ. (Use 2 decimal places.) lower limit upper limit
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? O x1 O X4 O x2 O x3 Which variables are the explanatory variables? (Select all that apply.) O x1 O X4 O X3 (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 = 6, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.) (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." 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 x, increased by 1 unit. What would be the corresponding change in x,? Suppose x2 increased by 2 units. What would be the expected change in x,? Suppose x2 decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.321. Construct a 99% confidence interval for the coefficient of xɔ. (Use 2 decimal places.) lower limit upper limit
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