For the data set shown below, complete parts (a) through (d) below. (a) Find the

Question

For the data set shown below, complete parts (a) through (d) below. (a) Find the estimates of beta_0 and beta_1. beta_0 almostequalto beta_0 = (Round to three decimal places as needed.) beta_1 almostequalto beta_1 = (Round to three decimal places as needed.) (b) Compute the standard error, the point estimate for sigma. s_e = (Round to four decimal places as needed.) (c) Assuming the residuals are normally distributed, determine s_b_1. s_b_1 = (Round to three decimal places as needed.) (d) Assuming the residuals are normally distributed, test H_0: beta_1 = 0 versus H_1: beta_1 notequalto 0 at the alpha = 0.05 level of significance. Use the P-value approach. The P-value for this test is (Round to three decimal places as needed.) Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below. Click to select your answer (s).

Explanation / Answer

a] bo = - 1.977

     b1 = 2.070

b] se = 0.6010

c] sb1 = 0.147

d] p-value = 0.001

by p-value approach, we reject the null hypothesis because alpha = 0.05 > p-value.

Reject Ho: There is sufficient evidence at alpha = 0.05, that a linear relation exists between X and Y.

Here all the calculation is done by MINITAB

Choose Stat > Regression > Regression.

In Response, enter Y.

In Predictors, enter X.

Go to Results: choose second option that is regression equation, table of coeifficents...

Click OK.

Session window output

MTB > Regress 'Y' 1 'X';
SUBC>   Constant;
SUBC>   Brief 1.

Regression Analysis: Y versus X

The regression equation is
Y = - 1.98 + 2.07 X

Predictor     Coef     SE Coef       T      P
Constant   -1.9767   0.8398     -2.35 0.100
     X           2.0698   0.1471     14.07 0.001

S = 0.609994   R-Sq = 98.5%   R-Sq(adj) = 98.0%
Analysis of Variance

Source            DF      SS        MS    F        P
Regression        1 73.684    73.684 198.03 0.001
Residual Error 3 1.116 0.372
Total               4     74.800

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