Use Minitab for this question. In Minitab , correlation is found under Stat/Basi
ID: 2936431 • Letter: U
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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.
Determine the value of the Pearson correlation coefficient between Y and X.
Determine the value of the Spearman correlation coefficient between Y and X.
Compute the values for the slope and intercept of the regression of Y on X.
What is B1 ?
What is B0 ?
Transform the weight data by taking the natural logarithm.
Determine the value of the Pearson correlation coefficient between transformed Y and X.
Determine the value of the Spearman correlation coefficient between transformed Y and X.
Compute the values for the slope and intercept of the regression of transformed Y on X.What is B1?
What is B0 ?
X 6 7 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 1.17 1.609 3.135Explanation / Answer
a) Correlation: X, Y
Pearson correlation of X and Y = 0.838
P-Value = 0.001
b)Spearman Rho: X, Y
Spearman rho for X and Y = 1.000
P-Value = *
c)
Regression Analysis: Y versus X
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 6.385 6.3846 21.15 0.001
X 1 6.385 6.3846 21.15 0.001
Error 9 2.716 0.3018
Total 10 9.101
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.549385 70.15% 66.84% 44.53%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -1.941 0.600 -3.24 0.010
X 0.2409 0.0524 4.60 0.001 1.00
Regression Equation
Y = -1.941 + 0.2409 X
B1= 0.2409
B0= -1.941
d)
Correlation: X, log(y)
Pearson correlation of X and log(y) = 0.999
P-Value = 0.000
e) Spearman Rho: X, log(y)
Spearman rho for X and log(y) = 1.000
P-Value = *
f) Regression Analysis: log(y) versus X
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 22.3964 22.3964 3442.72 0.000
X 1 22.3964 22.3964 3442.72 0.000
Error 9 0.0585 0.0065
Total 10 22.4550
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.0806563 99.74% 99.71% 99.57%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -6.1954 0.0880 -70.39 0.000
X 0.45122 0.00769 58.67 0.000 1.00
Regression Equation
log(y) = -6.1954 + 0.45122 X
B1 = 0.45122
B0 = -6.1954
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