Use the following linear regression equation to answer the questions. x 3 = 18.2

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.

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.)

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 = ±

Explanation / Answer

x3 = 18.2 + 4.4x1 + 8.2x4 1.2x7

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

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

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

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

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