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Linear Regression and Correlation: Confidence Interval for Mean

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1. The following sample observations were randomly selected.

X: 4, 5, 3, 6, 10
Y: 4, 6, 5, 7, 7

a. Determine the regression equation.

b. Determine the value of Y' when X is 7.

c. Determine the standard error of estimate.

d. Suppose a large sample is selected (instead of just 5). About 68% of the predictions would be between what two values?

e. Determine the .95 confidence interval for the mean predicted when X = 7.

f. Determine the .95 prediction interval for an individual predicted
when X = 7.

Please explain so that I can learn. Thanks.

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Solution Summary

Linear regression and correlation are determined. The .95 confidence interval for the mean predicted value is examined.

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Linear Regression and Correlation

See the attached file.

1. The following sample observations were randomly selected.

X: 4, 5, 3, 6, 10
Y: 4, 6, 5, 7, 7

a. Determine the regression equation.

b. Determine the value of Y' when X is 7.

c. Determine the standard error of estimate.

d. Suppose a large sample is selected (instead of just 5).
About 68% of the predictions would be between what two
values?

e. Determine the .95 confidence interval for the mean predicted when X = 7.

f. Determine the .95 prediction interval for an individual predicted
when X = 7.

Please explain so that I can learn.

Solution(a):

The required values for finding the intercept b0 and regression coefficient b1 are computed as ...

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