Question

16. Twenty-six observations are made for the random variables X and Y. Use the sums given below in answering the questions. Sxx = 591 Syy = 6600 Sxy = 1558 a. The coefficient of X is for the regression equation where Y is regressed on X. b. Find the test statistic and P-value for the hypothesis test. Ho: B = 0 H1: BE 0 Test Statistic: t = P-value:

Answer 1

Answer:

a)

Given,

Y = $\alpha$ + $\beta$ x

Estimate of coefficient of x is b = Sxy / Sxx = 1558/591 = 2.636

SSres = Syy - b*Sxy

substitute values

= 6600 - 2.636*1558

= 2493.112

Unbiased estimator s^2 = SSres^2 / (n-2)

substitute values

= 2493.112 / 24

= 103.87

b)

Ho : $\beta$ = 0

Ha : $\beta$ != 0

test statistic = (b - $\beta$ )/sqrt(s^2/Sxx)

substitute values

= 2.636/10.19

= 0.258

degrees of freedom = n - 2 = 26 - 2 = 24

P value = 0.798606

= 0.7986

Here we observe that, p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.