Use the following linear regression equation to answer the questions.
x_{1} = 1.5 + 3.5x_{2} –
8.2x_{3} + 2.1x_{4}
(a) Which variable is the response variable?
A. x_{3}
B. x_{1}
C. x_{2}
D. x_{4}
(b) Which variables are the explanatory variables?
(Select all that apply.)
A. x_{4}
B. x_{1}
C. x_{3}
D. x_{2}
(c) Which number is the constant term? List the
coefficients with their corresponding explanatory variables.
constant ____________ | |
x_{2} coefficient_________ | |
x_{3} coefficient_________ | |
x_{4} coefficient_________ |
(d) If x_{2} = 4,
x_{3} = 5, and x_{4} = 9, what is
the predicted value for x_{1}? (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 x_{3} and
x_{4} were held at fixed but arbitrary values and
x_{2} increased by 1 unit. What would be the
corresponding change in x_{1}? _________
(g) Suppose x_{2} increased by 2
units. What would be the expected change in
x_{1}?___________
(h) Suppose x_{2} decreased by 4
units. What would be the expected change in
x_{1}?____________
(I) Suppose that n = 18 data points were
used to construct the given regression equation and that the
standard error for the coefficient of x_{2} is
0.412. Construct a 99% confidence interval for the coefficient of
x_{2}. (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
x_{2} is different from zero. (Use 2 decimal
places.)
t___________________ | |
t critical ±___________ |
(k) Conclusion
A. Reject the null hypothesis, there is sufficient evidence that β_{2} differs from 0.
B. Reject the null hypothesis, there is insufficient evidence that β_{2} differs from 0.
C. Fail to reject the null hypothesis, there is insufficient evidence that β_{2} differs from 0.
D. Fail to reject the null hypothesis, there is sufficient evidence that β_{2} differs from 0.
(L) Explain how the conclusion of this test would
affect the regression equation.
A. If we conclude that β_{2} is not different from 0 then we would remove x_{1} from the model.
B. If we conclude that β_{2} is not different from 0 then we would remove x_{3} from the model.
C. If we conclude that β_{2} is not different from 0 then we would remove x_{2} from the model.
D. If we conclude that β_{2} is not different from 0 then we would remove x_{4} 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.
Get Answers For Free
Most questions answered within 1 hours.