This Question Contains 2 Different Problems Problem 1 In a simple linear regress

Question

This Question Contains 2 Different Problems

Problem 1

In a simple linear regression based on 30 observations, it is found that b1 = 3.21 and  = 1.79. Consider the hypotheses (Use Table 2):

H0: 1 = 0 and HA: 1 0.

a.

Calculate the value of the appropriate test statistic. (Round your answer to 2 decimal places.)

  Test statistic

Problem 2

When estimating a multiple regression model based on 30 observations, the following results were obtained. Use Table 2.

Coefficients

Standard Error

t Stat

p-value

Lower 95%

Upper 95%

  Intercept

152.40       

123.25       

1.24   

0.2256  

100.51     

405.31   

  x1

12.77       

2.79       

4.57   

9.67E-05

7.04     

18.50   

  x2

2.83       

2.43       

1.17   

0.2522

2.16     

7.82   

What is the 95% confidence interval for 2? (Negative values should be indicated by a minus sign.Round your intermediate calculations to 4 decimal places, "t/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

  Confidence interval

   to

In a simple linear regression based on 30 observations, it is found that b1 = 3.21 and  = 1.79. Consider the hypotheses (Use Table 2):

Explanation / Answer

1. We have b1 = 3.21 and SE = 1.79

The value of the appropriate test statistic for the t-test = (3.21-0)/1.79 = 1.79.

2. No.of degrees of freedom = 30-1 = 29

t/2, 0.975 = 2.05; t/2, 0.025 = -2.05;

One side width of the confidence interval = standard error x t/2, 0.975 = 2.43 x 2.05 =4.9815

Confidence interval = 2.83 ± 4.9815 =[2.83-4.9815, 2.83 + 4.9815] = [ -2.15, 7.81]

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