Chapter 9.4, Problem 1P

Statistical Literacy Given the linear regression equation

$x_{\text{1}}\text{ = 1}.\text{6 + 3}.\text{5}{x}_{\text{2}}-\text{ 7}.\text{9}{x}_{\text{3}}\text{ + 2}.0x_{\text{4}}$

1. (a) Which variable is the response variable? Which variables are the explanatory variables?
2. (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.
3. (c) If x₂ = 2, x₃ = 1, and x₄ = 5, what is the predicted value for x₁?
4. (d) Explain how each coefficient can be thought of as a “slope” under certain conditions. Suppose x₃ and x₄ were held at fixed but arbitrary values and x₂ was increased by 1 unit. What would be the corresponding change in x₁? Suppose x₂ increased by 2 units. What would be the expected change in x₁? Suppose x₂ decreased by 4 units. What would be the expected change in x₁?
5. (e) Suppose that n = 12 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.419. Construct a 90% confidence interval for the coefficient of x_2.
6. (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x₂ is different from zero. Explain how the conclusion of this test would affect the regression equation.