Question

Use the following linear regression equation to answer the questions.

x₃ = ?16.6 + 3.7x₁ + 8.6x₄ ? 1.9x₇

(a) Which variable is the response variable?

x₄

x₁    

x₃

x₇

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

x₄

x₇

x₁

x₃

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

constant=
x1 coefficient=
x4 coefficient =
x7 coefficient =

(c) If x₁ = 4, x₄ = -4, and x₇ = 9, what is the predicted value for x₃? (Round your answer to one decimal place.)
x₃ =  

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

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

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

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

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

Suppose x₁ and x₇ were held at fixed but arbitrary values.
If x₄ increased by 1 unit, what would we expect the corresponding change in x₃ to be?


If x₄ increased by 3 units, what would be the corresponding expected change in x₃?


If x₄ decreased by 2 units, what would we expect for the corresponding change in x₃?


(e) Suppose that n = 20 data points were used to construct the given regression equation and that the standard error for the coefficient of x₄ is 0.924. Construct a 90% confidence interval for the coefficient of x₄. (Round your answers to two decimal places.)

lower limit=
upper limit =

(f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x₄ is different from zero. (Round your answers to two decimal places.)

t	=
t critical	±

Conclusion

Reject the null hypothesis, there is sufficient evidence that ?₄ differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that ?₄ differs from 0.   

  Reject the null hypothesis, there is insufficient evidence that ?₄ differs from 0

.Fail to reject the null hypothesis, there is sufficient evidence that ?₄ differs from 0.

Explain how the conclusion has a bearing on the regression equation.

If we conclude that ?₄ is not different from 0 then we would remove x₁ from the model.

If we conclude that ?₄ is not different from 0 then we would remove x₇ from the model.   

  If we conclude that ?₄ is not different from 0 then we would remove x₄ from the model.

If we conclude that ?₄ is not different from 0 then we would remove x₃ from the model.

Answer 1

x3 = ?16.6 + 3.7x1 + 8.6x4 ? 1.9x7

(a) Which variable is the response variable?

x3
Which variables are the explanatory variables? (Select all that apply.)

x4,x7,x1

(b) Which number is the constant term? List the coefficients with their corresponding explanatory variables.
constant= -16.6  
x1 coefficient=       3.7
x4 coefficient =    8.6
x7 coefficient =    -1.9

(c) If x1 = 4, x4 = -4, and x7 = 9, what is the predicted value for x3? (Round your answer to one decimal place.)
x3 = -16.6 + 3.7x1 + 8.6x4 - 1.9x7
= -16.6 + 3.7 * 4 + 8.6 * (-4) -1.9 * 9
= -53.3

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

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

Suppose x1 and x7 were held at fixed but arbitrary values.
If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be?
increase by 8.6

If x4 increased by 3 units, what would be the corresponding expected change in x3?
increase by 8.6 *3 = 25.8

If x4 decreased by 2 units, what would we expect for the corresponding change in x3?
decrease by 8.6 *2 = 17.2

Post rest questions again

Maximum 4 subparts can be posted