Question

Use the following linear regression equation to answer the questions.

x₃ = −18.2 + 4.4x₁ + 8.2x₄ − 1.2x₇

Which number is the constant term? List the coefficients with their corresponding explanatory variables.

constant
x1 coefficient
x4 coefficient
x7 coefficient If x1 = 3, x4 = -9, and x7 = 6, what is the predicted value for x3? (Round your answer to one decimal place.) x3 =   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 = 19 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.847. 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 = ±

Answer 1

x₃ = −18.2 + 4.4x₁ + 8.2x₄ − 1.2x₇

Which number is the constant term? List the coefficients with their corresponding explanatory variables.

constant   -18.2
x1 coefficient      4.4
x4 coefficient    8.2
x7 coefficient   -1.2 If x1 = 3, x4 = -9, and x7 = 6, what is the predicted value for x3? (Round your answer to one decimal place.) x3 =   −18.2 + 4.4x1 + 8.2x4 − 1.2x7 = −18.2 + 4.4*3 + 8.2 * (-9) − 1.2*6 = -86 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? increase by 8.2 If x4 increased by 3 units, what would be the corresponding expected change in x3? increase by 8.2*3 = 24.6 If x4 decreased by 2 units, what would we expect for the corresponding change in x3? decrease by 8.2 *2 = 16.4 (e) Suppose that n = 19 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.847. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) df = n-k -1 = 19 -3-1 = 15 t = 1.753 lower limit      = (8.2 - 1.753 * 0.847) = 6.7152 upper limit = (8.2 + 1.753 * 0.847) = 9.684791 (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 = 8.2/0.847 = 9.68122 t critical = ± 2.131

we reject the null and conclude that the coefficient of x₄ is different from zero.