Question

# 19) Use the following linear regression equation to answer the questions. x3 = −18.7 + 4.3x1...

19) Use the following linear regression equation to answer the questions.

x3 = −18.7 + 4.3x1 + 8.6x4 − 1.0x7

(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 = 5, x4 = -6, and x7 = 4, what is the predicted value for x3? (Round your answer to one decimal place.)
x3 =

(d)

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 = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.946. 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 = ±

b)

 constant -18.7 x1 coeffiicent 4.3 x4 coefficient 8.6 x7 coeffiicent -1

c)

predicted value =-18.7+4.3*5+8.6*(-6)-1*4 =-52.8

d)

If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be =8.6

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

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

e)

 sample size n= 18 number of independent variables p= 3 degree of freedom =n-p-1= 14 estimated slope b= 8.6 standard error of slope=sb= 0.9460 for 90 % confidence and 14degree of freedom critical t= 1.7610 90% confidence interval =b1 -/+ t*standard error= (6.93,10.27)
 lower limit =6.93 upper limit=10.27

f)

t=8.6/0.946=9.09

tcritical= -/+ 2.98

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