MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Use the following linear regression equation to answer the
questions.
x3 = -18.8 + 4.0x, + 9.3x4 - 1.3x7
(a) Which variable is the response variable?
Which variables are the explanatory variables?
(b) Which number is the constant term? List the coefficients with
their corresponding explanatory variables.
(c) If X1
X3?
= 10, X4
= -4, and x7
= 4, what is the predicted value for
(d) Explain how each coefficient can be thought of as a "slope"
under certain conditions.
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 = 11 data points were used to construct the
given regression equation and that the standard error for the
is 0.857. Construct a 90% confidence
coefficient of
X4
interval for the coefficient of x4.
(f) Using the information of part (e) and level of significance 1%,
test the claim that the coefficient of x4 is different from zero.
Explain how the conclusion has a bearing on the regression
equation.
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Transcribed Image Text:Use the following linear regression equation to answer the questions. x3 = -18.8 + 4.0x, + 9.3x4 - 1.3x7 (a) Which variable is the response variable? Which variables are the explanatory variables? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. (c) If X1 X3? = 10, X4 = -4, and x7 = 4, what is the predicted value for (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. 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 = 11 data points were used to construct the given regression equation and that the standard error for the is 0.857. Construct a 90% confidence coefficient of X4 interval for the coefficient of x4. (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of x4 is different from zero. Explain how the conclusion has a bearing on the regression equation.
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