Consider the following set of ordered pairs. 3 Calculate the coefficient of dete

ID: 3075050 • Letter: C

Question

Consider the following set of ordered pairs. 3 Calculate the coefficient of determination and test its significance using 0.05. Click the icon to view a partial ANOVA table. Click the icon to view a partial table of critical F-scores with 0.05 in the right tail of the distribution. Calculate the coefficient of determination. R" = | | (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Choose the correct answer below. H1,p2 20 H: p2so Determine the critical F-score, Fa Fa (Round to three decimal places as needed.) Calculate the F-score for this test. F(Round to three decimal places as needed.) Determine the correct conclusion. Choose the correct answer below. O A. Reject Ho. There appears to be a relationship between x and y. O B. Do not reject Ho. There does not appear to be a relationship between x and y. O C. Do not reject Ho. There appears to be a relationship between x and y D. Reiect Ha. There does not annear to be a relationshin hetween x and v Click to select your answer(s)

Explanation / Answer

Solution

Preparatory Work

Mean X = Xbar = (1/n)sum of xi = 3.6

Mean Y = Ybar = (1/n)sum of yi = 3.6

Sxx = sum of (xi – Xbar)2 = 11.2

Syy = sum of (yi – Ybar)2 = 47.2

Sxy = sum of {(xi – Xbar)(yi – Ybar)} = 21.48

All above sums are over i = 1, 2, …., n,

n = sample size = 5

ANOVA TABLE

Source

MS = SS/df

Regression

44.004

MSR/MSE = 41.318

Error

3.196

1.065

Total

47.2

Part (a) Coefficient of Determination

R2 = (Sxy)2/{Sxx x Syy}

= 0.873 ANSWER

Part (b) Hypotheses

Testing for significance of Coefficient of Determination is testing if the population correlation coefficient square is zero or positive.

So, the null hypothesis is: H0: 2 = 0 and alternative is: H1: 2 > 0.

Since 2 cannot be negative, the above statement can also be written as: H0: 2 0 and H1: 2 > 0. Option B ANSWER

Part (c)

Under the null hypothesis, the test statistic, F ~ Fn, m, where n and m are degrees of freedom of the regression SS and error SS

Respectively in the ANOVA TABLE.

Thus, given level of significance as 5%, the critical value of F = upper 5% point of F1, 3

= 10.128 [from the given table] ANSWER

Part (d)

F – score = 41.318 [from ANOVA TABLE given under Preparatory Work] ANSWER

Part (e)

Conclusion

Since F – score > F – crit, H0 is rejected. => 2 is significant, i.e., 2 > 0 . Hence, the conclusion is:

There is sufficient evidence to suggest a relation between x and y. Option A ANSWER

DONE