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[Solution Library] Given the linear regression equation x_1=1.6+3.5 x_2-7.9 x_3+2.0 x_4 Which variable is the response variable? Which variables are the

Question: Given the linear regression equation

\[x_{1}=1.6+3.5 x_{2}-7.9 x_{3}+2.0 x_{4}\]
  1. Which variable is the response variable? Which variables are the explanatory variables?
  2. Which number is the constant term? List the coefficients with their corresponding explanatory variables.
  3. If \(x_{2}=2, x_{3}=1\), and \(x_{4}=5\), what is the predicted value for \(x_{1}\) ?
  4. Explain how each coefficient can be thought of as a "slope" under certain conditions. Suppose \(x_{3}\) and \(x_{4}\) were held at fixed but arbitrary values and \(x_{2}\) increased by one unit. What would be the corresponding change in \(x_{1}\) ? Suppose \(x_{2}\) increased by two units. What would be the expected change in \(x_{1}\) ? Suppose \(x_{2}\) decreased by four units. What would be the expected change in \(x_{1}\) ?
  5. Suppose that \(n=12\) data points were used to construct the given regression equation and that the standard error for the coefficient of \(x_{2}\) is $0.419 .$ Construct a \(90 \%\) confidence interval for the coefficient of \(x_{2}\).
  6. Using the information of part (e) and level of significance \(5 \%\), test the claim that the coefficient of \(x_{2}\) is different from zero. Explain how the conclusion of this test would affect the regression equation.

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Deliverable: Word Document


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