a. Use the formula below to calculate the coefficient of determination, R^2, whe

Question

a. Use the formula below to calculate the coefficient of determination, R^2, where SSR is the sum of squares regression and SST is the total sum of squares.

b. Determine the critical F-score, F, for =0.05 and degrees of freedom D1=1 and D2=2, corresponding to the degrees of freedom for the SSR and the sum of squares error, SSE, respectively. While either technology or an F-distribution table can be used to find the critical F-score, for this exercise, use a table to determine this value.

c. Determine the correct conclusion. If the F-test statistic is greater than the critical value of F, reject the null hypothesis and conclude that there appears to be a relationship between x and y. Otherwise, do not reject the null hypothesis.

Consider the following set of ordered pairs Calculate the coefficient of determination and test its significance using 0.05.

Explanation / Answer

a) Coefficient of determination will be = SSR/SST = 0.75/2.75 = 0.2727

(b) Here D1 = 1 snd D2 = 2 and Critical F value will be 18.513

(c) Since F test statistic less than Critical value, fail to reject the null hypothesis and conclude that there is no relationship between x and y

SUMMARY OUTPUT Regression Statistics Multiple R 0.5222 R Square 0.2727 Adjusted R Square -0.0909 Standard Error 1 Observations 4 ANOVA df SS MS F Significance F Regression 1 0.75 0.75 0.75 0.477767032 Residual 2 2 1 Total 3 2.75 Coefficients Standard Error t Stat P-value Lower 95% Intercept 4.000 4.359 0.918 0.456 -14.755 X Variable 1 1.000 1.155 0.866 0.478 -3.968

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