Consider the n = 11 data values in the following table. Suppose we consider the

Question

Consider the n = 11 data values in the following table.

Suppose we consider the simple normal linear regression to describe the relationship between the response Y and the predictor X.

a) Calculate the least-squares line

b) Predict a future Y at X = 0.0. Is this prediction an extrapolation or an interpolation? Determine the standard error of this prediction.

c) Predict a future Y at X = 6.0. Is this prediction an extrapolation or an interpolation? Determine the standard error of this prediction.

Explanation / Answer

From Excel

The fitted model is

y= -0.00091 +2.102(x)

b) when x=0

Then

y= -0.00091 +2.102(0)

y= -0.00091

c)

when x=6

Then

y= -0.00091 +2.102(6)

y=12.6111

SUMMARY OUTPUT Regression Statistics Multiple R 0.978673 R Square 0.957801 Adjusted R Square 0.953112 Standard Error 1.542756 Observations 11 ANOVA df SS MS F Significance F Regression 1 486.1926 486.1926 204.2743 1.72E-07 Residual 9 21.42088 2.380097 Total 10 507.6135 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.00091 0.465159 -0.00195 0.998483 -1.05317 1.051353 -1.05317 1.051353 X 2.102364 0.147096 14.29245 1.72E-07 1.769609 2.435118 1.769609 2.435118

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