In Minitab , correlation is found under Stat/Basic . Remember that a Spearman co
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Question
In Minitab, correlation is found under Stat/Basic. Remember that a Spearman correlation is the correlation of the ranks. To calculate the natural logarithms of the data contained in, say, column 2 and put the results in, say, column 3, do the following. Under Editor, click Enble Commands, then type Let C3 = log(C2) at the MTB prompt.
Dry weights (Y) of 11 chick embryos ranging in age from 6 to 16 days (X) are given below.
Use Minitab for this question. In Minitab, correlation is found under Stat/Basic. Remeber that a Spearman correlation is the correlation of the ranks. To calculate the natural logarithms of the data contained in, say, column 2 and put the results in, say, column 3, do the following. Under Editor, click Enble Commands, then type Let c3 log(C2 at the MTB prompt. Dry weights (Y) of 11 chick embryos ranging in age from 6 to 16 days (X) are given below. 6 8 9 10 11 12 13 14 15 16 Y 0.029 0.052 0.079 0.125 0.181 0.261 0.425 0.738 1.13 1.84 2.921 Determine the value of the Pearson correlation coefficient between Y and X. 2 pt(s)] Submit Answer Tries 0/3 Determine the value of the Spearman correlation coefficient between Y and X. 12 pt(s)] Submit Answer Tries 0/3 Compute the values for the slope and intercept of the regression of Y on X. What is B1? 2 pt( Submit Answer Tries 0/3 What is po? 2 pt(s Submit Answer Tries 0/3 Transform the weight data by taking the natural logarithm. 12 pt(s)] Determine the value of the Pearson correlation coefficient between transformed Y and X. Submit Answer Tries 0/3Explanation / Answer
To calculate spearmen's correlation, we have the below formula:-
1-(6Ed^2/n(n^2-1) and so the answer would be 1 in both the cases (normal and logged). We have calculated the data as below for calculating spearmen's correlation:-
Normal:-
Logged:-
Regression values (Normal):-
Pearson correlation coefficient is 0.855.
Spearmen correlation coefficient is 1.
B1=0.2385
B0=-1.91614
Regression values (Logged):-
Pearson correlation coefficient is 0.999.
Spearmen correlation coefficient is 1.
B1=0.4519
B0=-6.20069
X Y Rank (X) Rank (Y) d d^2 6 0.029 1 1 0 0 7 0.052 2 2 0 0 8 0.079 3 3 0 0 9 0.125 4 4 0 0 10 0.181 5 5 0 0 11 0.261 6 6 0 0 12 0.425 7 7 0 0 13 0.738 8 8 0 0 14 1.13 9 9 0 0 15 1.84 10 10 0 0 16 2.921 11 11 0 0Logged:-
X Y Logged Rank (X) Rank (Y) d d^2 6 0.029 -3.54046 1 1 0 0 7 0.052 -2.95651 2 2 0 0 8 0.079 -2.53831 3 3 0 0 9 0.125 -2.07944 4 4 0 0 10 0.181 -1.70926 5 5 0 0 11 0.261 -1.34323 6 6 0 0 12 0.425 -0.85567 7 7 0 0 13 0.738 -0.30381 8 8 0 0 14 1.13 0.122218 9 9 0 0 15 1.84 0.609766 10 10 0 0 16 2.921 1.071926 11 11 0 0Regression values (Normal):-
SUMMARY OUTPUT Regression Statistics Multiple R 0.855849 R Square 0.732478 Adjusted R Square 0.702753 Standard Error 0.503902 Observations 11 ANOVA df SS MS F Significance F Regression 1 6.257048 6.257048 24.64203 0.000776 Residual 9 2.285259 0.253918 Total 10 8.542307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.91614 0.549903 -3.4845 0.00689 -3.1601 -0.67217 -3.1601 -0.67217 X 0.2385 0.048045 4.964074 0.000776 0.129814 0.347186 0.129814 0.347186Pearson correlation coefficient is 0.855.
Spearmen correlation coefficient is 1.
B1=0.2385
B0=-1.91614
Regression values (Logged):-
SUMMARY OUTPUT Regression Statistics Multiple R 0.999171 R Square 0.998342 Adjusted R Square 0.998158 Standard Error 0.06438 Observations 11 ANOVA df SS MS F Significance F Regression 1 22.46753 22.46753 5420.647 7.96E-14 Residual 9 0.037303 0.004145 Total 10 22.50483 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -6.20069 0.070257 -88.2569 1.56E-14 -6.35962 -6.04176 -6.35962 -6.04176 X 0.451941 0.006138 73.62504 7.96E-14 0.438055 0.465827 0.438055 0.465827Pearson correlation coefficient is 0.999.
Spearmen correlation coefficient is 1.
B1=0.4519
B0=-6.20069
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