Use the following linear regression equation to answer the questions.
x3 = −15.6 + 3.8x1 + 9.1x4 − 1.5x7
(a) which variable is the response variable?
x1
x4
x7
x3

which variables are the explanatory variables? (select all that apply.)
x3
x7
x1
x4

(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 = -1, and x7 = 10, 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 look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.
if we look at all coefficients together, each one can be thought of as a "slope."
if we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope."
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 = 17 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.965. 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 5%, test the claim that the coefficient of x4 is different from zero. (round your answers to two decimal places.)
t =
t critical = ±

conclusion
fail to reject the null hypothesis, there is insufficient evidence that β4 differs from 0.
fail to reject the null hypothesis, there is sufficient evidence that β4 differs from 0.
reject the null hypothesis, there is sufficient evidence that β4 differs from 0.
reject the null hypothesis, there is insufficient evidence that β4 differs from 0.

explain how the conclusion has a bearing on the regression equation.
if we conclude that β4 is not different from 0 then we would remove x3 from the model.
if we conclude that β4 is not different from 0 then we would remove x7 from the model.
if we conclude that β4 is not different from 0 then we would remove x4 from the model.
if we conclude that β4 is not different from 0 then we would remove x1 from the model.