Use the following linear regression equation to answer the questions.
x_{1} = 1.7 + 3.6x_{2} – 7.7x_{3} + 2.4x_{4}
Which number is the constant term? List the coefficients with their corresponding explanatory variables.
constant | |
x_{2} coefficient | |
x_{3} coefficient | |
x_{4} coefficient |
If x_{2} = 1, x_{3} = 8, and x_{4} = 9, what is the predicted value for x_{1}? (Use 1 decimal place.)
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}?
Suppose x_{2} increased by 2 units. What would be
the expected change in x_{1}?
Suppose x_{2} decreased by 4 units. What would be
the expected change in x_{1}?
(e) Suppose that n = 11 data points were used to construct
the given regression equation and that the standard error for the
coefficient of x_{2} is 0.363. Construct a 99%
confidence interval for the coefficient of x_{2}.
(Use 2 decimal places.)
lower limit | |
upper limit |
(f) Using the information of part (e) and level of significance 5%,
test the claim that the coefficient of x_{2} is
different from zero. (Use 2 decimal places.)
t | |
t critical ± |
constant | 1.7 |
x_{2} coefficient | 3.6 |
x_{3} coefficient | -7.7 |
x_{4} coefficient | 2.4 |
x_{1} = 1.7 + 3.6x_{2} – 7.7x_{3} + 2.4x_{4}
_{= 1.7 + 3.6 - 7.7 *8 + 2.4 *9}
_{=} -34.7
x_{2} increased by 1 unit. What would be the corresponding change in x_{1}?
increase by 3.6
Suppose x_{2} increased by 2 units. What would be
the expected change in x_{1}?
increase by 3.6*2 = 7.2
Suppose x_{2} decreased by 4 units. What would be
the expected change in x_{1}?
decrease by 3.6 *4 = 14.4
e)
df = n-k -1 = 11 - 3-1 = 7
for 99 % confidence interval
t = 3.5
(3.6 - 3.5* 0.363 , 3.6 + 3.5 * 0.363)
=(2.3295 , 4.8705)
f) t = (3.6 - 0)/0.363 = 9.917
critical value = 2.365
9.917 > 2.365
we reject the null
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