Use the following linear regression equation to answer the questions.
x3 = −16.5 + 4.5x1 + 8.4x4 − 1.5x7
(a) Which variable is the response variable?
x4x3 x7x1
Which variables are the explanatory variables? (Select all that
apply.)
x4x7x3x1
(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 = 3, x4 = -10,
and x7 = 8, what is the predicted value for
x3? (Round your answer to one decimal
place.)
x3 =
(d) Explain how each coefficient can be thought of as a "slope"
under certain conditions.
If we hold all explanatory variables as fixed constants, the intercept can be thought of 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 other explanatory variables as fixed constants, then we can look at one coefficient as a "slope."
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 = 15 data points were used to construct
the given regression equation and that the standard error for the
coefficient of x4 is 0.996. 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 | = ± |
Use the following linear regression equation to answer the questions. x3 = −16.5 + 4.5x1 +...
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