Question

Use the following linear regression equation to answer the questions.

x₁ = 1.1 + 3.0x₂ – 8.4x₃ + 2.3x₄

(a) Which variable is the response variable?

x₃

x₁     

x₂

x₄

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

x₁

x₂

x₃

x₄

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

constant =
x2 coefficient=
x3 coefficient=
x4 coefficient=

(c) If x₂ = 4, x₃ = 10, and x₄ = 6, what is the predicted value for x₁? (Use 1 decimal place.)

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

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

If we look at all coefficients together, each one 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 explanatory variables as fixed constants, the intercept can be thought of as a "slope."

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?

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?


(e) Suppose that n = 13 data points were used to construct the given regression equation and that the standard error for the coefficient of x₂ is 0.391. Construct a 95% confidence interval for the coefficient of x₂. (Use 2 decimal places.)

lower limit=
upper limit =

(f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x₂ is different from zero. (Use 2 decimal places.)

t=
t critical ±	=

Conclusion

Reject the null hypothesis, there is sufficient evidence that ?₂ differs from 0.

Reject the null hypothesis, there is insufficient evidence that ?₂ differs from 0.    

Fail to reject the null hypothesis, there is insufficient evidence that ?₂ differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence that ?₂ differs from 0.

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

If we conclude that ?₂ is not different from 0 then we would remove x₃ from the model.If we conclude that ?₂ is not different from 0 then we would remove x₄ from the model.     

If we conclude that ?₂ is not different from 0 then we would remove x₁ from the model.If we conclude that ?₂ is not different from 0 then we would remove x₂ from the model.

Answer 1

Answer :

A) response variable = x1, it is the variable where the value calculated as a response from input is stored.

Explanatory variable : x2,x3 and x4. These are independent variables system is having.

B) constant term : 1.1

Coefficient of x2 = 3.0

Coefficient of x3 = -8.4

Coefficient of x4= 2.3

C) given x2 = 4, x3 = 10 and x4 = 6: then using given equation

X1 = 1.1 + 3.0*4 - 8.4*10+2.3* 6. = -57.1

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

Example : if x3 and x4 are zero that is de =0 and x4=0 than the coefficient of x2 will be the slope of the line and this is valid in all the other cases also.

If x3 and x4 are constant and de is increase by 1, then the x1 will get increase by the factor equals to coefficient of x2.