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The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

Respuesta :

Chrisnando

Answer:

t = ±2.179

Step-by-step explanation:

Given:

Regression equation = Y = 30 + 2.56X

Sample size, n = 14

Standard error, e = 0.97

Significance level, [tex] \alpha [/tex] = 0.05

Required:

Find the critical value

At level of significance = 0.05

Degrees of freedom, df = n - 2 = 14 - 2= 12

Find critical value:

Using t table, two tailed, df = 12, we have:

[tex] t_\alpha_/_2_, _d_f = t_0_._0_2_5_,_1_3 = 2.179 [/tex]

Therefore, the critical value,

t-critical = ±2.179

lhmarianateixeira

In this exercise we will use the knowledge of degrees of freedom and the data reported in the exercise to calculate the critical temperature of the system, so:

[tex]t-critical = +/- 2.179[/tex]

Given in the exercise we have to:

  • Regression equation: [tex]Y = 30 + 2.56X[/tex]
  • Sample size:  [tex]14[/tex]
  • Standard error:  [tex]0.97[/tex]
  • Significance level:  [tex]0.05[/tex]

in this exercise we want to find the critical value in this way, we will have that it will be:

  • At level of significance = 0.05
  • Degrees of freedom, df = n - 2 = 14 - 2= 12

Using t table, two tailed, df = 12, we have:

[tex]T_{\alpha /2} , df = t_{0.025,13)= 2.179[/tex]

Therefore, the critical value corresponde to;

[tex]t-critical = +/- 2.179[/tex]

See more about critical temperature at brainly.com/question/14562729

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