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### Example 173tech

Example 173 tech:  The Minitab output below is from a study looking at the sum of gingival pocket depths and arterial plaque scores for 30 individuals. A high value for the sum of the pocket depths indicates gum disease, and a high value for the arterial plaque score indicates heart disease. The results of the analysis are given below. Use the results to answer the questions that follow.
Analysis of Variance

Regression      1  3388.73  3388.73    86.04    0.000
Error          28  1102.74    39.38
Total          29  4491.47

Model Summary

6.27563  75.45%     74.57%

Coefficients

Term            Coef  SE Coef  T-Value  P-Value
Constant        7.77     2.23     3.48    0.002
PocketDepth  0.03161  0.00341     9.28    0.000

Regression Equation

PlaqueScore = 7.77 + 0.03161 * (PocketDepth)

a.    Find the least squares line. Is there a significant linear relationship? If so, is it positive or negative?
b.    Identify the MSE in the computer output
c.    Find the correlation coefficient. Interpret this value.
d.    Identify the coefficient of determination. Does it indicate that the sum of pocket depths is a strong predictor of arterial plaque scores?
e.    The following interval is a 95% confidence interval for the mean arterial plaque score for patients with a pocket depth sum of 538. Interpret the interval: (22.1, 27.4)
f.    The following interval is a 95% prediction interval for the arterial plaque score for a patient with a pocket depth sum of 538. Interpret the interval: (11.7, 37.9)
g.    The 30 values for the variable sum of pocket depths used in this problem ranged from 192 mm to 1,152 mm. Would it be wise to use this data to form a prediction interval for arterial plaque score for patients with a sum of pocket depths value of 1,325 mm?

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