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The accompanying table shows the regression results when estimating y = 0 + 1 x

ID: 3223396 • Letter: T

Question

The accompanying table shows the regression results when estimating y = 0 + 1x + .

df

SS

MS

F

Significance F

Regression

1

78.5900

78.5900

15.82

0.0106

Residual

5

24.8385

4.9677

Total

6

103.4286

Coefficients

Standard Error

t-stat

p-value

Intercept

15.6615

2.4020

6.520

0.0013

x

1.6927

0.4256

3.977

0.0106

a. Specify the competing hypotheses to determine whether x is significant in y.

b. At the 5% significance level, is x significant? Explain.

df

SS

MS

F

Significance F

Regression

1

78.5900

78.5900

15.82

0.0106

Residual

5

24.8385

4.9677

Total

6

103.4286

Coefficients

Standard Error

t-stat

p-value

Intercept

15.6615

2.4020

6.520

0.0013

x

1.6927

0.4256

3.977

0.0106

Explanation / Answer

a. Null Hypothesis : Ho : there is not a significant linear relationship between the independent variable X and the dependent variable Y and B1= 0

H1: there is a significant linear relationship between the independent variable X and the dependent variable Y and B1 0

b. Test Statistic :

t = b1 / SE = -1.6927/ 0.4256 = - 3.977

for alpha = 0.05 significance level tcritical = 2.571

where t >  tcriticalso null hypothesis is wrong and we can reject it and can say that there is a significant linear relationship between the independent variable X and the dependent variable Y and b1 0

We can also conclude that by checking respective p - value which is equal to 0.0106 < p = 0.05 .

So x is significant in y and linear relationship between two variables are significant.

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