Question

Exercise 15-6 Algo

When estimating a multiple linear regression model based on 30 observations, the following results were obtained. [You may find it useful to reference the t table.]

	Coefficients	Standard Error	t Stat	p-value
Intercept	153.35	126.57	1.212	0.236
x1	11.10	2.62	4.237	0.000
x2	2.36	2.06	1.146	0.261

a-1. Choose the hypotheses to determine whether x₁ and y are linearly related.

• H₀: β₁ = 0; H_A: β₁ ≠ 0

• H₀: β₀ = 0; H_A: β₀ ≠ 0

• H₀: β₀ ≤ 0; H_A: β₀ > 0

• H₀: β₁ ≤ 0; H_A: β₁ > 0

a-2. At the 5% significance level, when determining whether x₁ and y are linearly related, the decision is to:

• Reject H₀x₁ and y are linearly related.
• Reject H₀x₁ and y are not linearly related.
• Do not reject H₀we cannot conclude x₁ and y are linearly related.

b-1. What is the 95% confidence interval for β₂? (Negative values should be indicated by a minus sign. Round "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

b-2. Using this confidence interval, is x₂ significant in explaining y?

• No, since the interval does not contain zero.

• No, since the interval contains zero.

• Yes, since the interval does not contain zero.

• Yes, since the interval contains zero.

c-1. At the 5% significance level, choose the hypotheses to determine if β₁ is less than 20.

• H₀: β₁ ≥ 20; H_A: β₁ < 20

• H₀: β₁ ≤ 20; H_A: β₁ > 20

• H₀: β₁ = 20; H_A: β₁ ≠ 20

c-2. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

c-3. At the 5% significance level, can you conclude that β₁ is less than 20?

• Yes, since the null hypothesis is rejected.

• Yes, since the null hypothesis is not rejected.

• No, since the null hypothesis is not rejected.

• No, since the null hypothesis is rejected.

Answer 1

a-1. the hypotheses to determine whether x1 and y are linearly related.

H0: β1 = 0; HA: β1 ≠ 0

a-2. At the 5% significance level, when determining whether x1 and y are linearly related, the decision is to:

Reject H0

x1 and y are linearly related.

b-1. t at 95% with 28 df = 2.05

95% confidence interval for β2 is  β2 t SE

= 2.36   2.05*2.06 = 2.36  4.223 = (-1.86,6.58)

b-2. Using this confidence interval, is x2 significant in explaining y?

• No, since the interval contains zero

c-1.  the hypotheses to determine if β1 is less than 20.

H0: β1 ≥ 20; HA: β1 < 20

c-2. the value of the test statistic

= -8.563

p value =0.000

c-3. At the 5% significance level because p value is less than 0.05

• Yes, since the null hypothesis is rejected.