Question

Consider the following regression results based on 20 observations. [You may find it useful to reference the t table.]

	Coefficients	Standard Error	t Stat	p-value
Intercept	30.8201	4.6053	6.692	0.000
x1	0.3302	0.1804	1.830	0.084

a-1. Choose the hypotheses to determine if the intercept differs from zero.

• H₀: β₀ ≥ 0; H_A: β₀ < 0

• H₀: β₀ ≤ 0; H_A: β₀ > 0

• H₀: β₀ = 0; H_A: β₀ ≠ 0

a-2. At the 5% significance level, what is the conclusion to the hypothesis test? Does the intercept differ from zero?

• Reject H₀; the intercept is greater than zero.

• Reject H₀; the intercept differs from zero.

• Do not reject H₀; the intercept is greater than zero.

• Do not reject H₀; the intercept differs from zero.

b-1. Construct the 95% confidence interval for the slope coefficient. (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. At the 5% significance level, can we conclude the slope differs from zero?

• Yes, since the interval contains zero.

• Yes, since the interval does not contain zero.

• No, since the interval contains zero.

• No, since the interval does not contain zero.

Answer 1

a1.

since we have to test that if Intercept is different from Zero so the hypothesis is

a2)

Since P Value for Intercept is 0.00

which is less than level of significance (0.05) Hence we reject H0 hence we have enough evidence to conclude that intercept is differ from ZERO hence

Reject H0; the intercept differs from zero.

b1)

for slope we have

calculated slope =b=0.3302

standard error of "b" =SE=0.1804

n=20

since here we have two parameters hence DF=n-2=20-2=18

now 95% confidence interval for slope is given by

so interval is

(-0.0488,0.7092)

b2)

since P value for slope is 0.084 which is greater than level of significance (0.05) Hence we failed to reject H0 that is we don't have enough evidence to support the claim that slope is different from ZERO hence

also in confidence interval contains ZERO hence there is chance that slope can be ZERO too

hence

No, since the interval contains zero.