Use the following linear regression equation to answer the questions. X1 = 1.8 + 3.7x2 - 7.BX3 + 1.5x4 (a) Which variable is the response variable? O X 3 O X 1 O X 2 O X4 Which variables are the explanatory variables? (Select all that apply.) O X A O X 1 O X 2 O X3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X3 coefficient X4 coefficient (c) If X2 = 10, X3 = 7, and X4 = 4, what is the predicted value for x1 ? (Use 1 decimal place.) d) Explain how each coefficient can be thought of as a "slope" under certain conditions. 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, 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 look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line. Suppose x, and x were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x,? Suppose x, increased by 2 units. What would be the expected change in x, ? Suppose x, decreased by 4 units. What would be the expected change in x, ? (e) Suppose that n = 17 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.391. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.) lower limit upper limit