Question

Use the following linear regression equation to answer the questions. x1 = 1.5 + 3.5x2 –...

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.

(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.

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