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	31.4333	4.5131	6.965	0.000
x1	0.1987	0.1470	1.352	0.193

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

A-1)

A-2)

P VALUE FOR INTERCEPT = 0.000

P VALUE < 0.05,REJECT Ho

...

b-1)

confidence interval for slope                      
                      
n =   20                  
alpha,α =    0.05                  
estimated slope=   0.1987                  
std error =    0.147                  
                      
Df = n-2 =   18                  
t critical value =    2.101   [excel function: =t.inv.2t(α,df) ]              
                      
margin of error ,E = t*std error =    2.1009   *   0.147   =   0.3088  
                      
95%   confidence interval is ß1 ± E                   
lower bound = estimated slope - margin of error =    0.1987   -   0.3088   =   -0.11  
upper bound = estimated slope + margin of error =    0.1987   +   0.3088   =   0.51  
CI (-0.11 , 0.51 )

b-2)

...............

Please revert back in case of any doubt.

Please upvote. Thanks in advance.