Question

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	= ±

Answer 1

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 x_{3 =}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