Use the following linear regression equation to answer the questions. X3 = -17.5 + 4.3x, + 8.6X4 - 1.6X7 (a) Which variable is the response variable? OX z O X 4 O X 7 O X 1 Which variables are the explanatory variables? (Select all that apply.) X3 O X 1 0 X7 O X 4 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant x1 coefficient X4 coefficient X, coefficient (c) If x, = 9, X4 = -3, and x7 = 9, 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. O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient 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 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." Suppose x, and x7 were held at fixed but arbitrary values. If x 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 = 12 data points were used to construct the given regression equation and that the standard error for the coefficient of x Is 0.954. Construct a 90% confidence Interval for the coefficient of X. (Round your answers to two decimal places.) lower limit upper limit