Question

Significance level of 0.05, test whether the slope of the regression line is negative. The regression...

Significance level of 0.05, test whether the slope of the regression line is negative.

The regression equation is, Y = 6.0 - 0.7x

predictor           coef               stdev          t-ratio

constant            6.0                2.558           2.32

X                      -0.7                0.086            -8.28

ANOVA

source           df                ss                    ms                F

regression      1               648.12                648.12           68.58

error               6                56.72                 9.45

total               7              704.84

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Answer #1

ANSWER:

GIVEN THAT

  Significance level of 0.05

  The regression equation is, Y = 6.0 - 0.7 x

  • We need to test if the slope is negative.

       n = Total d+ 1 = 7 + 1 = 8

        n=8

  • Hence, Degrees of freedom for slope testing = n - 2 = 8 - 2 = 6
  • This is a left tailed test so critical t value at 0.05 significance level = -1.943
  • Obtained t value from output = -8.28 since -8.28 is less than the critical value, we reject Ho.
  • Therefore, we can conclude that the slope of the regression line is negative.
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