Question

Use the following linear regression equation to answer the questions.

x₁ = 1.5 + 3.5x₂ – 8.2x₃ + 2.1x₄

(a) Which variable is the response variable?

A. x₃

B. x₁    

C. x₂

D. x₄

(b) Which variables are the explanatory variables? (Select all that apply.)

A. x₄

B. x₁

C. x₃

D. x₂

(c) Which number is the constant term? List the coefficients with their corresponding explanatory variables.

constant ____________
x2 coefficient_________
x3 coefficient_________
x4 coefficient_________

(d) If x₂ = 4, x₃ = 5, and x₄ = 9, what is the predicted value for x₁? (Use 1 decimal place.) _____________

(e) Explain how each coefficient can be thought of as a "slope" under certain conditions.

A. If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."

B. If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.   

C. If we look at all coefficients together, each one can be thought of as a "slope."

D. If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope."

(f) Suppose x₃ and x₄ were held at fixed but arbitrary values and x₂ increased by 1 unit. What would be the corresponding change in x₁? _________


(g) Suppose x₂ increased by 2 units. What would be the expected change in x₁?___________


(h) Suppose x₂ decreased by 4 units. What would be the expected change in x₁?____________


(I) 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 0.412. Construct a 99% confidence interval for the coefficient of x₂. (Use 2 decimal places.)

lower limit_________
upper limit_________

(J) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x₂ is different from zero. (Use 2 decimal places.)

t___________________
t critical ±___________

(k) Conclusion

A. Reject the null hypothesis, there is sufficient evidence that β₂ differs from 0.

B. Reject the null hypothesis, there is insufficient evidence that β₂ differs from 0.    

C. Fail to reject the null hypothesis, there is insufficient evidence that β₂ differs from 0.

D. Fail to reject the null hypothesis, there is sufficient evidence that β₂ differs from 0.

(L) Explain how the conclusion of this test would affect the regression equation.

A. If we conclude that β₂ is not different from 0 then we would remove x₁ from the model.

B. If we conclude that β₂ is not different from 0 then we would remove x₃ from the model.   

C. If we conclude that β₂ is not different from 0 then we would remove x₂ from the model.

D. If we conclude that β₂ is not different from 0 then we would remove x₄ from the model.

Answer 1

(a) Answer is option B. x1 is the response variable, because its value is calculated based on changes in other values.

(b) Answers are A,C,D. Because, x2,x3 and x4 values are independent and determines the value of x1.

(c) Constant = 1.5

x2 coefficient = 3.5

x3 coefficient = -8.2

x4 coefficient = 2.1

(d) Value of x1 when x2 = 4, x3 = 5 and x4 = 9 is,

x1 = 1.5 + (3.5*4) - (8.2*5) + (2.1*9) = 1.5+14-41+18.9 = -6.6

We solve only 4 questions in one post. Please post again for other solutions.