Question

A. Draw a scatter plot of these data, with the number of earthworm species as the predictor/explanatory variable.

B. Using the following summary calculations, calculate the regression line.

̅̅
X = 2.205 Y = 0.215

̅2̅2̅̅ ∑(X−X) =86.359 Σ(Y−Y) =0.366 ∑(X−X)(Y−Y)=2.453

What is the slope of the line?

What is the intercept of the line?

If the MSerror (=MSresidual) is 0.0080, then what is the SE of the slope?

What is the upper 95% CI for the slope?

What is the predicted nitrogen content of soil with five earthworm species?

In regression analysis, what does a decreasing r2 value mean?

Number of earthworm species Total nitrogen content(%) 0.22,0.19,0.16, 0.08, 0.05 0.33, 0.30, 0.26, 0.24, 0.20 0.27, 0.24, 0.23, 0.18, 0.16, 0.13 0.40, 0.32, 0.32, 0.29, 0.24, 0.22, 0.12 0.34, 0.33, 0.23, 0.21, 0.18, 0.17, 0.15, 0.14 0.54, 0.20 0 2 4

Answer 1

Using

The regression equation is
Number of earthworm species = 1.137 + 5.558 *Total Nitrogen Content(%)

The slope of the line = 5.558

The intercept of the line=1.137

ME = critical value * standard error

( Critical value from t table at 95% CI for degrees of freedom = 6-2 = 4 )

Standard Error = 0.0080/2.132 = 0.00375

The predicted nitrogen content of soil with five earthworm species:

Number of earthworm species = 1.137 + 5.558 *Total Nitrogen Content(%)

=> 5 = 1.137 + 5.558* Total Nitrogen Content(%)

=> Total Nitrogen Content(%) = (5-1.137)/5.558 = 0.6950

A decreasing r2 value means that the model explains the responses.

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