Use the following linear regression equation to answer the questions.X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4(a) Which variable is the response variable?O X4O X2O 3Which variables are the explanatory variables? (Select all that apply.)O 3O X4O X1O ×2(b) Which number is the constant term? List the coefficients with theircorresponding explanatory variables.constantX2 coefficientX, coefficientX4 coefficient(c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,?(Use 1 decimal place.)(d) Explain how each coefficient can be thought of as a "slope" undercertain conditions.O If we look at all coefficients together, each one can be thought of asa "slope."O If we hold all explanatory variables as fixed constants, the interceptcan be thought of as a "slope."O If we hold all other explanatory variables as fixed constants, thenwe can look at one coefficient as a "slope."O If we look at all coefficients together, the sum of them can bethought of as the overall "slope" of the regression line. Suppose x3 and x4 were held at fixed but arbitrary values and x,increased by 1 unit. What would be the corresponding change in x,?Suppose x, increased by 2 units. What would be the expected change inX1?Suppose x, decreased by 4 units. What would be the expected changein x1?(e) Suppose that n = 16 data points were used to construct the givenregression equation and that the standard error for the coefficient of x,is 0.307. Construct a 95% confidence interval for the coefficient of x,.(Use 2 decimal places.)lower limitupper limit(f) Using the information of part (e) and level of significance 1%, testthe claim that the coefficient of xɔ is different from zero. (Use 2 decimalplaces.)t critical +ConclusionO Reject the null hypothesis, there is sufficient evidence that ß, differsfrom 0.O Reject the null hypothesis, there is insufficient evidence that ß,differs from 0.O Fail to reject the null hypothesis, there is insufficient evidence thatB2 differs from 0.O Fail to reject the null hypothesis, there is sufficient evidence that ß,differs from 0.Explain how the conclusion of this test would affect the regressionequation.O If we conclude that B, is not different from 0 then we would removeX3 from the model.O If we conclude that ß, is not different from 0 then we would removeX1 from the model.O If we conclude that ß, is not different from 0 then we would removeX4 from the model.O If we conclude that B, is not different from 0 then we would removeX2 from the model.

Question

Use the following linear regression equation to answer the questions.X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4(a) Which variable is the response variable?O X4O X2O 3Which variables are the explanatory variables? (Select all that apply.)O 3O X4O X1O ×2(b) Which number is the constant term? List the coefficients with theircorresponding explanatory variables.constantX2 coefficientX, coefficientX4 coefficient(c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,?(Use 1 decimal place.)(d) Explain how each coefficient can be thought of as a &#34;slope&#34; undercertain conditions.O If we look at all coefficients together, each one can be thought of asa &#34;slope.&#34;O If we hold all explanatory variables as fixed constants, the interceptcan be thought of as a &#34;slope.&#34;O If we hold all other explanatory variables as fixed constants, thenwe can look at one coefficient as a &#34;slope.&#34;O If we look at all coefficients together, the sum of them can bethought of as the overall &#34;slope&#34; of the regression line. Suppose x3 and x4 were held at fixed but arbitrary values and x,increased by 1 unit. What would be the corresponding change in x,?Suppose x, increased by 2 units. What would be the expected change inX1?Suppose x, decreased by 4 units. What would be the expected changein x1?(e) Suppose that n = 16 data points were used to construct the givenregression equation and that the standard error for the coefficient of x,is 0.307. Construct a 95% confidence interval for the coefficient of x,.(Use 2 decimal places.)lower limitupper limit(f) Using the information of part (e) and level of significance 1%, testthe claim that the coefficient of xɔ is different from zero. (Use 2 decimalplaces.)t critical +ConclusionO Reject the null hypothesis, there is sufficient evidence that ß, differsfrom 0.O Reject the null hypothesis, there is insufficient evidence that ß,differs from 0.O Fail to reject the null hypothesis, there is insufficient evidence thatB2 differs from 0.O Fail to reject the null hypothesis, there is sufficient evidence that ß,differs from 0.Explain how the conclusion of this test would affect the regressionequation.O If we conclude that B, is not different from 0 then we would removeX3 from the model.O If we conclude that ß, is not different from 0 then we would removeX1 from the model.O If we conclude that ß, is not different from 0 then we would removeX4 from the model.O If we conclude that B, is not different from 0 then we would removeX2 from the model.

Accepted Answer

Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

(a) Which variable is the respon O X1 O X2 X3