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Use the following linear regression equation to answer the questions. X3 = -17.9 + 3.7x, + 8.4X4 - 1.8x7 (a) Which variable is the response variable? O X 4 O X- OX3 Which variables are the explanatory variables? (Select all that apply.) O X 1 VX3 V X- J X4 X (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant coefficient 4 coefficient X7 coefficient (c) If x1 = 3, X4 = -3, and x, = 1, what is the predicted value for x3? (Round your answer to one 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 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 . If we look at all coefficients together, each one can be thought of as a "slope." Suppose x, and x, 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 x increased by 3 units, what would be the corresponding expected change in X3? If x decreased by 2 units, what would we expect for the corresponding change in x3? (e) Suppose that n = 20 data points were used to construct the given regression equation and that the standard error for the coefficient of x is 0.874. 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 three decimal places.) t critical = + Conclusion O Reject the null hypothesis, there is insufficient evidence that B differs from 0. O Reject the null hypothesis, there is sufficient evidence that B4 differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that B 4 differs from 0. Fail to reject the null hypothesis, there is insufficient evidence that B 4 differs from 0. Explain how the conclusion has a bearing on the regression equation. O If we conclude that B4 is not different from 0 then we would remove x, from the model. If we conclude that B4 is not different from 0 then we would remove x, from the model. O If we conclude that B is not different from 0 then we would remove x3 from the model. If we conclude that B4 is not different from 0 then we would remove x4 from the model. Need Help? Master It