The following table is the output of simple linear regressio

The following table is the output of simple linear regression analysis. Note that in the lower right hand corner of each output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H₀: ?₁ = 0 versus H_a: ?₁ ? 0.

Use the explained variation and the unexplained variation as given on the above table to calculate the F(model) statistic. (Round your answer to 4 decimal places.)

Utilize the F(model) statistic and the appropriate critical value to test H₀: ?₁ = 0 versus H_a: ?₁ ? 0 by setting ? equal to .05. What do you conclude about the regression relationship between y and x?

Utilize the F(model) statistic and the appropriate critical value to test H₀: ?₁ = 0 versus H_a: ?₁ ? 0 by setting ? equal to .01. What do you conclude about the regression relationship between y and x?

Find the p-value related to F(model) on the above table and report its value. Using the p-value, test the significance of the regression model at the .10, .05, .01, and .001 levels of significance. What do you conclude?

Solution

The following table is the output of simple linear regression analysis. Note that in the lower right hand corner of each output we give (in parentheses) the number of observations, n, used to perform the regression analysis and the t statistic for testing H₀: ?₁ = 0 versus H_a: ?₁ ? 0.

  ANOVA

df

SS

MS

F

Significance F

  Regression

1

1,020,892.9043

1,020,892.9043

15,311.1949

0

  Residual Error

10

666.7624

66.6762

  Total

10

1,021,559.6667

(n=12; t=123.7384)

(a)

Use the explained variation and the unexplained variation as given on the above table to calculate the F(model) statistic. (Round your answer to 4 decimal places.)

  F = 15311.1949

(b)

Utilize the F(model) statistic and the appropriate critical value to test H₀: ?₁ = 0 versus H_a: ?₁ ? 0 by setting ? equal to .05. What do you conclude about the regression relationship between y and x?

  (Click to select)Reject H₀ with strong evidence of a significant relationship between x and y

(c)

Utilize the F(model) statistic and the appropriate critical value to test H₀: ?₁ = 0 versus H_a: ?₁ ? 0 by setting ? equal to .01. What do you conclude about the regression relationship between y and x?

  (Click to selectReject H₀ with very strong evidence of a significant relationship between x and y

(d)

Find the p-value related to F(model) on the above table and report its value. Using the p-value, test the significance of the regression model at the .10, .05, .01, and .001 levels of significance. What do you conclude?

  p-value = 0.0000

; (Click to select)Reject H₀ at ? = 0.001